Strongly Correlated Electrons
- [1] arXiv:2405.09611 [pdf, ps, html, other]
-
Title: Fermionic quantum criticality through the lens of topological holographyComments: 33 pages, 7 figures, 6 tablesSubjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
We utilize the topological holographic framework to characterize and gain insights into the nature of quantum critical points and gapless phases in fermionic quantum systems. Topological holography is a general framework that describes the generalized global symmetry and the symmetry charges of a local quantum system in terms of a slab of a topological order, termed as the symmetry topological field theory (SymTFT), in one higher dimension. In this work, we consider a generalization of the topological holographic picture for $(1+1)d$ fermionic quantum phases of matter. We discuss how spin structures are encoded in the SymTFT and establish the connection between the formal fermionization formula in quantum field theory and the choice of fermionic gapped boundary conditions of the SymTFT. We demonstrate the identification and the characterization of the fermionic gapped phases and phase transitions through detailed analysis of various examples, including the fermionic systems with $\mathbb{Z}_{2}^{F}$, $\mathbb{Z}_{2} \times \mathbb{Z}_{2}^{F}$, $\mathbb{Z}_{4}^{F}$, and the fermionic version of the non-invertible $\text{Rep}(S_{3})$ symmetry. Our work uncovers many exotic fermionic quantum critical points and gapless phases, including two kinds of fermionic symmetry enriched quantum critical points, a fermionic gapless symmetry protected topological (SPT) phase, and a fermionic gapless spontaneous symmetry breaking (SSB) phase that breaks the fermionic non-invertible symmetry.
- [2] arXiv:2405.09616 [pdf, ps, html, other]
-
Title: Theory of possible sliding regimes in twisted bilayer WTe$_2$Comments: Main text: 9 pages with 3 figures and 1 table. Supplementary material: 26 pages with 6 figures and 1 tableSubjects: Strongly Correlated Electrons (cond-mat.str-el); Materials Science (cond-mat.mtrl-sci); Superconductivity (cond-mat.supr-con)
Inspired by the observation of increasingly one-dimensional (1D) behavior with decreasing temperature in small-angle twisted bilayers of WTe$_2$ (tWTe$_2$), we theoretically explore the exotic sliding regimes that could be realized in tWTe$_2$. At zero displacement field, while hole-doped tWTe$_2$ can be thought of as an array of weakly coupled conventional two-flavor 1D electron gases (1DEGs), the electron-doped regime is equivalent to coupled four-flavor 1DEGs , due to the presence of an additional "valley'' degree of freedom. In the decoupled limit, the electron-doped system can thus realize phases with a range of interesting ordering tendencies, including $4k_F$ charge-density-wave and charge-$4e$ superconductivity. Dimensional crossovers and cross-wire transport due to inter-wire couplings of various kinds are also discussed. We find that a sliding Luther-Emery liquid with small inter-wire couplings is probably most consistent with current experiments on hole-doped tWTe$_2$.
- [3] arXiv:2405.09627 [pdf, ps, html, other]
-
Title: Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal LimitComments: 5 pages, 3 figuresSubjects: Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
In the presence of strong electronic interactions, a partially filled Chern band may stabilize a fractional Chern insulator (FCI) state, the zero-field analog of the fractional quantum Hall phase. While FCIs have long been hypothesized, feasible solid-state realizations only recently emerged, largely due to the rise of moiré materials. In these systems, the quantum geometry of the electronic bands plays a critical role in stabilizing the FCI in the presence of competing correlated phases. In the limit of ``ideal'' quantum geometry, where the quantum geometry is identical to that of Landau levels, this role is well understood. However, in more realistic scenarios only empiric numerical evidence exists, accentuating the need for a clear understanding of the mechanism by which the FCI deteriorates moving further away from these ideal conditions. We introduce and analyze an anisotropic model of a $\left|C \right|=1$ Chern insulator, whereupon partial filling of its bands, an FCI phase is stabilized over a certain parameter regime. We incorporate strong electronic interaction analytically by employing a coupled-wires approach, studying the FCI stability and its relation to the the quantum metric. We identify an unusual anti-FCI phase benefiting from non-ideal geometry, generically subdominant to the FCI. However, its presence hinders the formation of FCI in favor of other competitive phases at fractional fillings, such as the charge density wave. Though quite peculiar, this anti-FCI phase may have already been observed in experiments at high magnetic fields. This establish a direct link between quantum geometry and FCI stability in a tractable model far from any ideal band conditions, and illuminates a unique mechanism of FCI deterioration.
- [4] arXiv:2405.09665 [pdf, ps, other]
-
Title: Sign-Alternating Thermoelectric Quantum Oscillations and Insulating Landau Levels in Monolayer WTe2Yue Tang, Tiancheng Song, Haosen Guan, Yanyu Jia, Guo Yu, Zhaoyi Joy Zheng, Ayelet J. Uzan, Michael Onyszczak, Ratnadwip Singha, Xin Gui, Kenji Watanabe, Takashi Taniguchi, Robert J. Cava, Leslie M. Schoop, N. P. Ong, Sanfeng WuComments: 19 pages, 9 figuresSubjects: Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
The detection of Landau-level-like energy structures near the chemical potential of an insulator is essential to the search for a class of correlated electronic matter hosting charge-neutral fermions and Fermi surfaces, a long-proposed concept that remains elusive experimentally. Here we introduce and demonstrate that the magneto-thermoelectric response of a quantum insulator can reveal critical information not available via other approaches. We report large quantum oscillations (QOs) in the Seebeck response of the hole-doped insulating state of monolayer tungsten ditelluride (WTe2) in magnetic fields. The QOs remarkably undergo sign-changes as the field is swept, mimicking those in metals with Landau quantization. The sign-change in the thermoelectric response directly implies the presence of a field-induced Landau-level-like structure at the chemical potential of the insulator. Our results reinforce WTe2 as a platform for investigating insulating Landau levels and mobile neutral fermions in two-dimensional insulators.
- [5] arXiv:2405.09666 [pdf, ps, other]
-
Title: The Detection of Unconventional Quantum Oscillations in Insulating 2D MaterialsComments: 11 Pages, accepted to 2D MaterialsSubjects: Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
In strongly correlated quantum materials, electrons behave in ways that often extend beyond the confines of conventional Fermi-liquid theory. Interesting results include the observation of low-temperature metallic behavior in systems that are highly resistive. Here we provide an overview of experiments in which insulators exhibit characteristics of a metal such as the Shubnikov de Haas like quantum oscillations, focusing on recent findings in the correlated insulating states of two-dimensional WTe2. We discuss the status of current research, clarify the debates and challenges in interpreting the experiments, rule out extrinsic explanations and discuss promising future directions.
- [6] arXiv:2405.09877 [pdf, ps, html, other]
-
Title: Electron delocalization in a 2D Mott insulatorCosme G. Ayani, Michele Pisarra, Iván M. Ibarburu, Clara Rebanal, Manuela Garnica, Fabián Calleja, Fernando Martín, Amadeo L. Vázquez de PargaComments: 15 pages, 4 figuresSubjects: Strongly Correlated Electrons (cond-mat.str-el)
The prominent role of electron-electron interactions in two-dimensional (2D) materials versus three-dimensional (3D) ones is at the origin of the great variety of fermionic correlated states reported in the literature. In this respect, artificial van der Waals heterostructures comprising single layers of highly correlated insulators allow one to explore the effect of the subtle interlayer interaction in the way electrons correlate. In this work, we study the temperature dependence of the electronic properties of a van der Waals heterostructure composed of a single-layer Mott insulator lying on a metallic substrate by performing quasi-particle interference (QPI) maps. We show the emergence of a Fermi contour in the 2D Mott insulator at temperatures below 11K, which we attribute to the delocalization of the Mott electrons associated with the formation of a quantum coherent Kondo lattice. This Kondo lattice introduces a new periodicity in the system, so that the resulting Fermi surface encompasses both the substrate conduction electrons and the now delocalized correlated electrons from the 2D Mott insulator. Density Functional Theory calculations allow us to pinpoint the scattering vectors responsible for the experimentally observed quasi-particle interference maps, thus providing a complete picture of the delocalization of highly correlated electrons in a 2D Mott insulator.
- [7] arXiv:2405.10174 [pdf, ps, html, other]
-
Title: 3D-2D crossover and phase shift of beats of quantum oscillations of interlayer magnetoresistance in quasi-2D metalsComments: 13 pagesSubjects: Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Magnetic quantum oscillations (MQO) are traditionally applied to investigate the electronic structure of metals. In layered quasi-two-dimensional (Q2D) materials the MQO have several qualitative features giving additional useful information, provided their theoretical description is developed. Within the framework of the Kubo formula and the self-consistent Born approximation, we reconsider the phase of beats in the amplitude of Shubnikov oscillations of interlayer conductivity in Q2D metals. We show that the phase shift of beats of the Shubnikov (conductivity) oscillations relative to the de Haas - van Alphen (magnetization) oscillations is larger than expected previously and, under certain conditions, can reach the value of $\pi/2$, as observed experimentally. We explain the phase inversion of MQO during the 3D - 2D crossover and predict the decrease of relative MQO amplitude of interlayer magnetoresistance in a strong magnetic field, larger than the beat frequency.
- [8] arXiv:2405.10230 [pdf, ps, html, other]
-
Title: Universal entanglement correction induced by relevant deformations at the quantum critical pointSubjects: Strongly Correlated Electrons (cond-mat.str-el)
Local relevant deformations are important tool to study universal properties of quantum critical points. We investigate the effect of small relevant deformations on the bi-partite entanglement entropy at the quantum critical points. Within the quantum critical region, a universal power-law correction in the entanglement entropy induced by the relevant operator is found in both one- and two-dimensional critical lattice models. The exponent of the power-law correction term is determined by the scaling dimension of the relevant operator. Based on numerical simulations and scaling theory argument, it is conjectured that such a universal power-law correction in the entanglement entropy is universal for Lorentz invariant quantum critical points. Without Lorentz invariance, it is found the exponent in the power-law correction term does not fit in with the scaling argument in models with a dynamical exponent z=2 in two dimension. This may be because the relevant operator added in the lattice model corresponds to complicated operators in the corresponding conformal field theory. Our study provides a different perspective to extract universal information of quantum critical points. We expect it would be useful to detect unique properties of topological quantum phase transitions.
New submissions for Friday, 17 May 2024 (showing 8 of 8 entries )
- [9] arXiv:2405.09614 (cross-list from hep-th) [pdf, ps, html, other]
-
Title: Positivity bounds on electromagnetic properties of mediaComments: 27 pages + appendices, 7 figuresSubjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The equations of motion for the average electromagnetic field in a medium -- the macroscopic Maxwell equations -- can be derived from the in-in effective action and the effect of the medium is encoded in the electric and magnetic permeabilities $\varepsilon(\omega,|\boldsymbol{k}|)$ and $\mu(\omega,|\boldsymbol{k}|)$. Microcausality implies analyticity of the retarded Green's functions when the imaginary part of the $4$-vector $(\omega,\boldsymbol{k})$ lies in forward light cone. With appropriate assumptions about the behavior of the medium at high frequencies one derives dispersion relations, originally studied by Leontovich. In the case of dielectrics these relations, combined with the positivity of the imaginary parts, imply bounds on the low-energy values of the response, $\varepsilon(0,0)$ and $\mu(0,0)$. In particular the quantities $\varepsilon(0,0)-1$ and $\varepsilon(0,0) - 1/\mu(0,0)$ are constrained to be positive and equal to integrals over the imaginary parts of the response. We discuss various improvements of these bounds in the case of non-relativistic media and with additional assumptions about the UV behavior.
- [10] arXiv:2405.09615 (cross-list from quant-ph) [pdf, ps, other]
-
Title: Characterizing MPS and PEPS Preparable via Measurement and FeedbackSubjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
Preparing long-range entangled states poses significant challenges for near-term quantum devices. It is known that measurement and feedback (MF) can aid this task by allowing the preparation of certain paradigmatic long-range entangled states with only constant circuit depth. Here we systematically explore the structure of states that can be prepared using constant-depth local circuits and a single MF round. Using the framework of tensor networks, the preparability under MF translates to tensor symmetries. We detail the structure of matrix-product states (MPS) and projected entangled-pair states (PEPS) that can be prepared using MF, revealing the coexistence of Clifford-like properties and magic. Furthermore, we provide analytic solutions to states exhibiting MF symmetries akin to the symmetry-protected topological order in one dimension and the topological order in two dimensions, and we discuss their characteristics. Finally, we discuss the analogous implementation of operators via MF, providing a structural theorem that connects to the well-known Clifford teleportation.
- [11] arXiv:2405.09617 (cross-list from cond-mat.mes-hall) [pdf, ps, html, other]
-
Title: Three-dimensional quantum Hall states as a chiral electromagnetic filterComments: 5 pages, 3 figuresSubjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el)
Extensive research has explored the optical properties of topological insulating materials, driven by their inherent stability and potential applications. In this study, we unveil a novel functionality of three-dimensional integer quantum Hall (3D IQH) states as broad-band filters for circularly polarized light, particularly effective in the terahertz (THz) frequency range under realistic system parameters. We also investigate the impact of practical imperfections, demonstrating the resilience of this filtering effect. Our findings reveal that this phenomenon is independent of the microscopic origin of the 3D IQH state, prompting discussions on its feasibility across diverse candidate materials. These results contribute to our understanding of fundamental optical properties and hold promise for practical applications in optical technologies.
- [12] arXiv:2405.09628 (cross-list from quant-ph) [pdf, ps, other]
-
Title: Quantum Dynamics in Krylov Space: Methods and ApplicationsPratik Nandy, Apollonas S. Matsoukas-Roubeas, Pablo Martínez-Azcona, Anatoly Dymarsky, Adolfo del CampoComments: 64 pages, 27 figures. arXiv admin note: text overlap with arXiv:1802.02633 by other authorsSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Chaotic Dynamics (nlin.CD)
The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide a compact and computationally efficient description of quantum evolution, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems.
- [13] arXiv:2405.09718 (cross-list from math-ph) [pdf, ps, html, other]
-
Title: Landscapes of integrable long-range spin chainsComments: 37 pages, 3 figures, 1 tableSubjects: Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI)
We clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains.
We evaluate various limits. More precisely, we tweak the MZ chain to allow for a short-range limit, and show it is the XX model with q-deformed antiperiodic boundary conditions. Taking $q\to 1$ gives the elliptic spin chain of Sechin and Zotov (SZ), whose trigonometric case is due to Fukui and Kawakami. It, too, can be adjusted to admit a short-range limit, which we demonstrate to be the antiperiodic XX model. By identifying the translation operator of the MZ chain, which is nontrivial, we show that antiperiodicity is a persistent feature.
We compare the resulting (vertex-type) landscape of the MZ chain with the (face-type) landscape containing the Heisenberg XXX and Haldane--Shastry chains. We find that the landscapes only share a single point: the rational Haldane--Shastry chain. Using wrapping we show that the SZ chain is the antiperiodic version of the Inozemtsev chain in a precise sense, and expand both chains around their nearest-neighbour limits to facilitate their interpretations as long-range deformations. - [14] arXiv:2405.09728 (cross-list from cond-mat.stat-mech) [pdf, ps, html, other]
-
Title: Hidden zero modes and topology of multiband non-Hermitian systemsSubjects: Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
In a finite non-Hermitian system, the number of zero modes does not necessarily reflect the topology of the system. This is known as the breakdown of the bulk-boundary correspondence and has lead to misconceptions about the topological protection of edge modes in such systems. Here we show why this breakdown does occur and that it typically results in hidden zero modes, extremely long-lived zero energy excitations, which are only revealed when considering the singular value instead of the eigenvalue spectrum. We point out, furthermore, that in a finite multiband non-Hermitian system with Hamiltonian $H$, one needs to consider also the reflected Hamiltonian $\tilde H$, which is in general distinct from the adjoint $H^\dagger$, to properly relate the number of protected zeroes to the winding number of $H$.
- [15] arXiv:2405.09751 (cross-list from hep-th) [pdf, ps, html, other]
-
Title: Gravitational Chern-Simons form and Chiral Gravitational Anomaly in Fluid MechanicsComments: 5 pagesSubjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el)
We show that the hydrodynamics of the perfect fluid admit a deformation that includes a chiral gravitational (or mixed) anomaly alongside the chiral anomaly. The deformation features a Wess- Zumino functional which involves the gravitational Chern-Simons term.
- [16] arXiv:2405.09754 (cross-list from hep-th) [pdf, ps, other]
-
Title: Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTsComments: 49 pagesSubjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el)
We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion supercategories, which are fusion $\pi$-supercategories with a choice of fermion parity. The aim of this paper is to flesh out the categorical Landau paradigm for fermionic symmetries. We use the formalism of Symmetry Topological Field Theory (SymTFT) to study possible gapped and gapless phases for such symmetries, along with possible deformations between these phases, which are organized into a Hasse phase diagram. The phases can be characterized in terms of sets of condensed, confined and deconfined generalized symmetry charges, reminiscent of notions familiar from superconductivity. Many of the gapless phases also serve as phase transitions between gapped phases. The associated fermionic conformal field theories (CFTs) can be obtained by performing generalized fermionic Kennedy-Tasaki (KT) transformations on bosonic CFTs describing simpler transitions. The fermionic non-invertible symmetries along with their charges and phases discussed here can be obtained from those of bosonic non-invertible symmetries via fermionization or Jordan-Wigner transformation, which is discussed in detail.
- [17] arXiv:2405.09840 (cross-list from cond-mat.supr-con) [pdf, ps, html, other]
-
Title: Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductorsComments: 13 pages, 7 figuresSubjects: Superconductivity (cond-mat.supr-con); Materials Science (cond-mat.mtrl-sci); Strongly Correlated Electrons (cond-mat.str-el)
We investigate the anomalous thermal Hall effect (ATHE) in Weyl superconductors realized by the $E_{1u}$ ($p$-wave and $f$-wave) chiral superconducting order for the point group $D_{6h}$. Using the quasiclassical Eilenberger theory, we analyze the influence of the impurity scattering and the line nodal excitations on the ATHE, and compare it with the intrinsic (topological) contribution. Because the transverse response is sensitive to the slope of the density of states at the Fermi surface, the extrinsic ATHE vanishes in both the weak (Born) and strong (unitarity) scattering limits. The thermal Hall conductivity (THC) is maximal at intermediate impurity strengths when there is a large slope of the density states in the impurity bands close to the Fermi energy. Under these conditions, the extrinsic ATHE dominates the intrinsic ATHE even at low temperatures. The extrinsic ATHE is sensitive to line nodal excitations, whereas the intrinsic ATHE is not. When the line nodes in the gap involve the sign change of the order parameter, the extrinsic contribution to the THC is suppressed even though the phase space for low energy excitation is large. In contrast, if the nodes are not accompanied by such a sign change, the extrinsic ATHE is significantly enhanced. Our results form a basis for the comprehensive analysis of anomalous thermal transport in Weyl superconductors.
- [18] arXiv:2405.09853 (cross-list from hep-th) [pdf, ps, html, other]
-
Title: Chiral symmetry breaking in the pseudo-quantum electrodynamics with non-Abelian four-fermion interactionsComments: 9 pages, 4 figuresSubjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el)
In the context of 2+1 dimensional Dirac materials, we consider electromagnetic interactions alongside a type of spin-dependent Hubbard interaction. The former is described by PQED theory, while the latter corresponds to an effective theory represented by the $SU(N_c)$ Thirring model. Employing Hubbard-Stratonovich transformation and large N expansion in the model yields a non-local $SU(N_c)$ Yang-Mills action. Subsequently, we solve Schwinger-Dyson equations to obtain the self-energy function of the fermion propagator, from which we determine the critical fermion flavor number $N^c_f$ and critical fine structure constant $\alpha_c$ indicative of chiral symmetry breaking. Our findings suggest that as the non-Abelian color number $N_c$ increases, the minimum value of the critical fermion flavor number monotonically increases, while the maximum value of the critical fine structure constant decreases accordingly, rendering the system more susceptible to chiral symmetry breaking.
- [19] arXiv:2405.10285 (cross-list from hep-lat) [pdf, ps, html, other]
-
Title: Interacting chiral fermions on the lattice with matrix product operator normsJutho Haegeman, Laurens Lootens, Quinten Mortier, Alexander Stottmeister, Atsushi Ueda, Frank VerstraeteSubjects: High Energy Physics - Lattice (hep-lat); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
We develop a formalism for simulating one-dimensional interacting chiral fermions on the lattice without breaking any local symmetries by defining a Fock space endowed with a semi-definite norm defined in terms of matrix product operators. This formalism can be understood as a second-quantized form of Stacey fermions, hence providing a possible solution for the fermion doubling problem and circumventing the Nielsen-Ninomiya theorem. We prove that the emerging theory is hermitian by virtue of the fact that it gives rise to a hermitian generalized eigenvalue problem and that it has local features as it can be simulated using tensor network methods similar to the ones used for simulating local quantum Hamiltonians. We also show that the scaling limit of the free model recovers the chiral fermion field. As a proof of principle, we consider a single Weyl fermion on a periodic ring with Hubbard-type nearest-neighbor interactions and construct a variational generalized DMRG code demonstrating that the ground states of the system for large system sizes can be determined efficiently.
- [20] arXiv:2405.10306 (cross-list from quant-ph) [pdf, ps, html, other]
-
Title: Fault Tolerance Embedded in a Quantum-Gap-Estimation Algorithm with Trial-State OptimizationComments: 5 pages, 3 figures, 1 tableSubjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
We construct a hybrid quantum algorithm to estimate gaps in many-body energy spectra and prove that it is inherently fault-tolerant to global multi-qubit depolarizing noise. Using trial-state optimization without active error correction, we show that the spectral peak of an exact target gap can be amplified beyond the noise threshold, thereby reducing gap-estimate error. We numerically verify fault tolerance using the Qiskit Aer simulator with a model of common mid-circuit noise channels. Our results reveal the potential for accurate quantum simulations on near-term noisy quantum computers.
Cross submissions for Friday, 17 May 2024 (showing 12 of 12 entries )
- [21] arXiv:2309.13301 (replaced) [pdf, ps, html, other]
-
Title: Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical pointsComments: 13 pages; 19 figuresSubjects: Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con)
We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.
- [22] arXiv:2311.18005 (replaced) [pdf, ps, html, other]
-
Title: Exact fixed-point tensor network construction for rational conformal field theoryComments: 12 pages, 13 figures, 4 tables; typos corrected, references added, more data included in AppendixSubjects: Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)
The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the "boundary-changing operators" on triangles. Our construction fully captures all the real-space RG conditions. We also provide a concrete example using the Ising model to compute the scaling dimensions explicitly based on the corresponding FP tensor. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door towards understanding CFT in higher dimensions.
- [23] arXiv:2402.01562 (replaced) [pdf, ps, other]
-
Title: Magnetism of CuCr$_2$X$_4$ (X= S and Se) spinels studied with muon spin rotation and relaxation ($\mu$SR)Comments: 17 pages, 10 Figures, experimental resultsSubjects: Strongly Correlated Electrons (cond-mat.str-el)
We present muon spin rotation and relaxation ($\mu$SR) results for chalcogenide spinels CuCr$_2$X$_4$ with X= S and Se. Both compounds are known as ferromagnetic metals with high Curie temperatures. Our $\mu$SR and magnetization data show clear signatures for additional magnetic transitions far below the respective Curie temperatures. They can be related to changes in the Cr valence system from the mixed valence between Cr$^{3+}$ and Cr$^{4+}$ at high temperatures and collinear ferromagnetism to a charge-ordered state at low temperatures with a different ferromagnetic structure. Our results demonstrate that the electronic systems and the related spin structures of both compounds are more complex than assumed so far.
- [24] arXiv:2403.17069 (replaced) [pdf, ps, other]
-
Title: Tensor network formulation of symmetry protected topological phases in mixed statesComments: Appendix D is fixedSubjects: Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix. In one dimension, we introduce strong injective matrix product density operators (MPDO), which describe a broad class of short-range correlated mixed states, including the locally decohered SPT states. We map strong injective MPDO to a pure state in the doubled Hilbert space and define the SPT phases according to the cohomology class of the symmetry group in the doubled state. Although the doubled state exhibits an enlarged symmetry, the possible SPT phases are also constrained by the Hermiticity and the semi-positivity of the density matrix. We here obtain a complete classification of SPT phases with a direct product of strong $G$ and weak $K$ unitary symmetry given by the cohomology group $H^2(G, \text{U}(1))\oplus H^1(K, H^1(G, \text{U}(1)))$. The SPT phases in our definition are preserved under symmetric local circuits consisting of non-degenerate channels. This motivates an alternative definition of SPT phases according to the equivalence class of mixed states under a ``one-way" connection using symmetric non-degenerate channels. In locally purifiable MPDO with strong symmetry, we prove that this alternative definition reproduces the cohomology classification. We further extend our results to two-dimensional mixed states described by strong semi-injective tensor network density operators and classify the possible SPT phases.
- [25] arXiv:2405.05302 (replaced) [pdf, ps, html, other]
-
Title: Illustrating the Categorical Landau Paradigm in Lattice ModelsComments: 4.5 pages + appendices, v2: references addedSubjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Recent years have seen the concept of global symmetry extended to non-invertible (or categorical) symmetries, for which composition of symmetry generators is not necessarily invertible. Such non-invertible symmetries lead to a generalization of the standard Landau paradigm. In this work we substantiate this framework by providing a (1+1)d lattice model, whose gapped phases and phase transitions can only be explained by symmetry breaking of non-invertible symmetries.
- [26] arXiv:2405.05964 (replaced) [pdf, ps, other]
-
Title: Lattice Models for Phases and Transitions with Non-Invertible SymmetriesComments: 76 pages + appendices; v2: references addedSubjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Non-invertible categorical symmetries have emerged as a powerful tool to uncover new beyond-Landau phases of matter, both gapped and gapless, along with second order phase transitions between them. The general theory of such phases in (1+1)d has been studied using the Symmetry Topological Field Theory (SymTFT), also known as topological holography. This has unearthed the infrared (IR) structure of these phases and transitions. In this paper, we describe how the SymTFT information can be converted into an ultraviolet (UV) anyonic chain lattice model realizing in the IR limit these phases and transitions. In many cases, the Hilbert space of the anyonic chain is tensor product decomposable and the model can be realized as a quantum spin-chain Hamiltonian. We also describe operators acting on the lattice models that are charged under non-invertible symmetries and act as order parameters for the phases and transitions. In order to fully describe the action of non-invertible symmetries, it is crucial to understand the symmetry twisted sectors of the lattice models, which we describe in detail. Throughout the paper, we illustrate the general concepts using the symmetry category $\mathsf{Rep}(S_3)$ formed by representations of the permutation group $S_3$, but our procedure can be applied to any fusion category symmetry.
- [27] arXiv:2405.08149 (replaced) [pdf, ps, other]
-
Title: A thorough investigation of the Antiferromagnetic ResonanceComments: 12 pages, 5 figuresSubjects: Strongly Correlated Electrons (cond-mat.str-el)
Antiferromagnetic (AF) compounds possess distinct characteristics that render them promising candidates for advancing the application of spin degrees of freedom in computational devices. For instance, AF materials exhibit minimal susceptibility to external magnetic fields while operating at frequencies significantly higher than their ferromagnetic counterparts. However, despite their potential, there remains a dearth of understanding, particularly concerning certain aspects of AF spintronics. In particular, the properties of coherent states in AF materials have received insufficient investigation, with many features extrapolated directly from the ferromagnetic scenario. Addressing this gap, this study offers a comprehensive examination of AF coherent states, shedding new light on both AF and Spin-Flop phases. Employing the Holstein-Primakoff formalism, we conduct an in-depth analysis of resonating-driven coherent phases. Subsequently, we apply this formalism to characterize antiferromagnetic resonance, a pivotal phenomenon in spin-pumping experiments, and extract crucial insights therefrom.
- [28] arXiv:2405.08386 (replaced) [pdf, ps, other]
-
Title: Robust non-Abelian even-denominator fractional Chern insulator in twisted bilayer MoTe$_2$Comments: Error in dataSubjects: Strongly Correlated Electrons (cond-mat.str-el)
A recent experiment observes a series of quantum Hall effects in transition metal dichalcogenide moiré MoTe$_2$ [K. Kang, et. al, Nature 628, 522-526 (2024)]. Among them, the filling $\nu$ = 3 state points to a time-reversal pair of edge states resembling those of the even-denominator fractional Chern insulators (FCI). Inspired by this discovery, we investigate whether a robust incompressible quantum Hall liquid can be stabilized in the half-filled Chern band of twisted MoTe$_2$ bilayers. We use the continuum model with parameters relevant to twisted MoTe$_2$ bilayers and obtain three consecutive nearly flat Chern bands that resemble the experimental plateaus at filling $\nu$ = 2, 4, 6. Crucially, when the second moiré miniband is half-filled, signatures of non-Abelian states are found via exact diagonalization calculations, including the stable six-fold ground state degeneracy which grows more robust for larger lattice sizes in consistency with an even-denominator FCI state. We further perform flux insertion simulations to reveal a 1/2 quantized many-body Chern number. Furthermore, the ground state density structure factors show no sharp peak, which excludes the charge density wave order. These evidences signal the potential of realizing the non-Abelian state at zero magnetic field in twisted MoTe$_2$ bilayers at the fractional hole filling 3/2.
- [29] arXiv:2209.06191 (replaced) [pdf, ps, html, other]
-
Title: Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuitsComments: V2: Published version. Contains improved main theorem and other minor modificationsSubjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read `sideways', i.e., along the spatial direction. Here, we show that this provides the ideal framework to understand and expand on the notion of measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We show how the dual-unitary dynamics generated by the dynamics of the paradigmatic one-dimensional kicked Ising chain with certain parameter choices generate resource states for universal deterministic MBQC. Specifically, after $k$ time-steps, equivalent to a depth-$k$ quantum circuit, we obtain a resource state for universal MBQC on $\sim 3k/4$ encoded qubits. Our protocol allows generic quantum circuits to be `rotated' in space-time and gives new ways to exchange between resources like qubit number and coherence time in quantum computers. Beyond the practical advantages, we also interpret the dual-unitary evolution as generating an infinite sequence of new symmetry-protected topological phases with spatially modulated symmetries, which gives a vast generalization of the well-studied one-dimensional cluster state and shows that our protocol is robust to symmetry-respecting deformations.
- [30] arXiv:2310.06698 (replaced) [pdf, ps, html, other]
-
Title: Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum AnnealerComments: 12 + 6 pages, 7 + 8 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
The presence of competing interactions due to geometry leads to frustration in quantum spin models. As a consequence, the ground state of such systems often displays a large degeneracy that can be lifted due to thermal or quantum effects. One such example is the antiferromagnetic Ising model on the Kagome lattice. It was shown that while the same model on the triangular lattice is ordered at zero temperature for small transverse field due to an order by disorder mechanism, the Kagome lattice resists any such effects and exhibits only short range spin correlations and a trivial paramagnetic phase. We embed this model on the latest architecture of D-Wave's quantum annealer, the Advantage2 prototype, which uses the highly connected Zephyr graph. Using advanced embedding and calibration techniques, we are able to embed a Kagome lattice with mixed open and periodic boundary conditions of 231 sites on the full graph of the currently available prototype. Through forward annealing experiments, we show that under a finite longitudinal field the system exhibits a one-third magnetization plateau, consistent with a classical spin liquid state of reduced entropy. An anneal-pause-quench protocol is then used to extract an experimental ensemble of states resulting from the equilibration of the model at finite transverse and longitudinal field. This allows us to construct a partial phase diagram and confirm that the system exits the constrained Hilbert space of the classical spin liquid when subjected to a transverse field. We connect our results to previous theoretical results and quantum Monte Carlo simulation, which helps us confirm the validity of the quantum simulation realized here, thereby extracting insight into the performance of the D-Wave quantum annealer to simulate non-trivial quantum systems in equilibrium.
- [31] arXiv:2310.16709 (replaced) [pdf, ps, html, other]
-
Title: Sampling reduced density matrix to extract fine levels of entanglement spectrumSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
Low-lying entanglement spectrum provides the quintessential fingerprint to identify the highly entangled quantum matter with topological and conformal field-theoretical properties. However, when the entangling region acquires long boundary with the environment, such as that between long coupled chains or in two or higher dimensions, there unfortunately exists no universal yet practical method to compute the entanglement spectra with affordable computational cost. Here we propose a new scheme to overcome such difficulty and successfully extract the low-lying fine entanglement spectrum (ES). We trace out the environment via quantum Monte Carlo simulation and diagonalize the reduced density matrix to gain the ES. We demonstrate the strength and reliability of our method through long coupled spin chains and answer its long-standing controversy. Our simulation results, with unprecedentedly large system sizes, establish the practical computation scheme of the entanglement spectrum with a huge freedom degree of environment.
- [32] arXiv:2312.16284 (replaced) [pdf, ps, html, other]
-
Title: Massless Lifshitz Field Theory for Arbitrary $z$Comments: 28 pages, 6 figures, minor modifications and 1 appendix added; to appear in JHEPSubjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el)
By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index $z$. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary $z$ using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the $c$-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a $z$-dependent radius scale for the Lifshitz background. This relation is consistent with the $z$-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.
- [33] arXiv:2402.17627 (replaced) [pdf, ps, html, other]
-
Title: Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methodsComments: 16 pages, 5 figures, 5 tablesSubjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); Nuclear Theory (nucl-th); Quantum Physics (quant-ph)
Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.
- [34] arXiv:2403.18333 (replaced) [pdf, ps, other]
-
Title: Quantum gravity of the Heisenberg algebraComments: 30 pages + appendices; v2: typos corrected, references addedSubjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); General Relativity and Quantum Cosmology (gr-qc)
We consider a simplified model of double scaled SYK (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory in its own right. We study properties of the emergent geometry including its dynamics in response to inserting matter particles. In particular, we find that the model displays de Sitter-like properties such as that infalling matter reduces the rate of growth of geodesic slices between the two boundaries. The simplicity of the model allows us to compute the full generating functional for correlation functions of the length mode or any number of matter operators. We provide evidence that the effective action of the geodesic length between boundary points is non-local. Furthermore, we use the on-shell solution for the geodesic lengths between any two boundary points to reconstruct an effective bulk metric and reverse engineer the dilaton gravity theory that generates this metric as a solution.
- [35] arXiv:2403.19597 (replaced) [pdf, ps, html, other]
-
Title: Reference Energies for Double Excitations: Improvement and ExtensionComments: 25 pages, 3 figures (Supporting Information available)Subjects: Chemical Physics (physics.chem-ph); Materials Science (cond-mat.mtrl-sci); Strongly Correlated Electrons (cond-mat.str-el); Nuclear Theory (nucl-th)
In the realm of photochemistry, the significance of double excitations (also known as doubly-excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [this http URL Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly-excited states where the transitions almost exclusively involve doubly-excited configurations and (ii) 19 "partial" doubly-excited states which exhibit a more balanced character between singly- and doubly-excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition ($\%T_1$) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.
- [36] arXiv:2405.07970 (replaced) [pdf, ps, html, other]
-
Title: How much entanglement is needed for emergent anyons and fermions?Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary for emergent anyons and fermions by using the geometric entanglement measure (GEM) which quantifies the maximal overlap between a given state and any short-range entangled states. For systems with emergent anyons, based on the braiding statistics, we show that the GEM scales linearly in the system size regardless of microscopic details. The phenomenon of emergent anyons can also be understood within the framework of quantum error correction (QEC). Specifically, we show that the GEM of any 2D stabilizer codes must be at least quadratic in the code distance. Our proof is based on a generic prescription for constructing string operators, establishing a rigorous and direct connection between emergent anyons and QEC. For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge and their coding properties could be rather poor, we show that the GEM also scales linearly in the system size. Our results also establish an intriguing link between quantum anomaly and entanglement: a quantum state respecting anomalous $1$-form symmetries, be it pure or mixed, must be long-range entangled and have large GEM, offering a non-trivial class of intrinsically mixed state phases.