Entanglement spectrum of topological insulators and superconductors

Abstract

We study two a priori unrelated constructions: the spectrum of edge modes in a band topological insulator or superconductor with a physical edge, and the ground state entanglement spectrum in an extended system where an edge is simulated by an entanglement bipartition. We prove an exact relation between the ground state entanglement spectrum of such a system and the spectrum edge modes of the corresponding spectrally flattened Hamiltonian. In particular, we show that degeneracies of the entanglement spectrum correspond to gapless edge modes.

4 pages, 1 figure. v4

References in corpus (12)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Reduced density matrices and entanglement entropy in free lattice models
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entropy scaling and simulability by Matrix Product States
• The entanglement gap and a new principle of adiabatic continuity
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Topological order in paired states of fermions in two-dimensions with breaking of parity and time-reversal symmetries
• Band Topology of Insulators via the Entanglement Spectrum

Cited by in corpus (309)

• Classification of topological quantum matter with symmetries
• Non-Hermitian Physics
• Higher-Order Topological Insulators
• Topological phases of non-Hermitian systems
• Towards a derivation of holographic entanglement entropy
• Topological phases of fermions in one dimension
• Quantum entanglement in condensed matter systems
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Inversion Symmetric Topological Insulators
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Quantum Entanglement in Neural Network States
• Relative Entropy and Holography
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Quantum coherence and geometric quantum discord
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Classification of Interacting Topological Floquet Phases in One Dimension
• Bulk-Edge Correspondence in the Entanglement Spectra
• Non-local order in gapless systems: Entanglement Spectrum in Spin Chains
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Extracting Excitations From Model State Entanglement
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• A geometric proof of the equality between entanglement and edge spectra
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Edge modes in band topological insulators
• Identification of symmetry-protected topological states on noisy quantum computers
• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• How universal is the entanglement spectrum?
• Power-Law Entanglement Spectrum in Many-Body Localized Phases
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Topological phases and phase transitions on the square-octagon lattice
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Many-body approach to non-Hermitian physics in fermionic systems
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Topology of one dimensional quantum systems out of equilibrium
• Topological Phase Transitions for Interacting Finite Systems
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Floquet dynamical phase transition and entanglement spectrum
• Twisted and untwisted negativity spectrum of free fermions
• Exceptional Bound States and negative Entanglement Entropy
• Negativity spectrum of one-dimensional conformal field theories
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Long-range topological insulators and weakened bulk-boundary correspondence
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Topological charge pumping in the interacting bosonic Rice-Mele model
• On topological phases of spin chains
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Finite-temperature mutual information in a simple phase transition
• Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
• Entanglement spectroscopy on a quantum computer
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Twist operators in higher dimensions
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Entanglement Hamiltonian of Interacting Fermionic Models
• Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
• Evaluation of ranks of real space and particle entanglement spectra for large systems
• Entanglement spectrum of one-dimensional extended Bose-Hubbard models
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• Classification of topological insulators and superconductors out of equilibrium
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Topological phases in gapped edges of fractionalized systems
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Entanglement topological invariants for one-dimensional topological superconductors
• Bound states and entanglement in the excited states of quantum spin chains
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• Entanglement spectra of complex paired superfluids
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• On the relation between entanglement and subsystem Hamiltonians
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Edge theories in Projected Entangled Pair State models
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Characterizing disordered fermion systems using the momentum-space entanglement spectrum
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Modular commutator in gapped quantum many-body systems
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Universalities of thermodynamic signatures in topological phases
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• Holographic duality between $(2+1)$-d quantum anomalous Hall state and $(3+1)$-d topological insulators
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Type-II quadrupole topological insulators
• On the continuum limit of the entanglement Hamiltonian
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Universal quantum criticality in static and Floquet-Majorana chains
• Universal entanglement spectrum in gapless symmetry protected topological states
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• Qubit-efficient entanglement spectroscopy using qubit resets
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Entanglement Spectroscopy using Quantum Monte Carlo
• Entanglement Spectrum of Su-Schrieffer-Heeger-Hubbard Model
• Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Negativity Spectrum in the Random Singlet Phase
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Bulk Topological Proximity Effect
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Topological Insulators and Quantum Spin Liquids
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Measuring entanglement entropy and its topological signature for phononic systems
• Multivariate trace estimation in constant quantum depth
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology
• Exploring interacting topological insulator of extended Su-Schrieffer-Heeger model
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Topological dynamics of gyroscopic and Floquet lattices from Newton's laws
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• Position momentum Duality in the Entanglement Spectrum of Free Fermions
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• Surface codes, quantum circuits, and entanglement phases
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Polarization and entanglement spectrum in non-hermitian systems
• Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models
• Optimal free descriptions of many-body theories
• Signatures of topology in quantum quench dynamics and their interrelation
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• An emergent geometric description for a topological phase transition in the Kitaev superconductor model
• Embedded Topological Insulators
• Multipartite-Entanglement Tomography of a Quantum Simulator
• Topological invariant for two-dimensional open systems
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• First-Order Topological Quantum Phase Transition in a Strongly Correlated Ladder
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach
• Topological phases in odd-legs frustrated synthetic ladders
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Entanglement properties of the time periodic Kitaev Chain
• Density-Matrix Renormalization Group Study of Kitaev--Heisenberg Model on a Triangular Lattice
• Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra
• Edge mode manipulation through commensurate multifrequency driving
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Equality of bulk wave functions and edge correlations in topological superconductors: A spacetime derivation
• Entanglement Entropy & Anomaly Inflow
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Visualizing Quasiparticles from Quantum Entanglement for general 1D phases
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Entanglement Spectrum of a Random Partition: Connection with the Localization Transition
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
• Tensor Network Implementation of Bulk Entanglement Spectrum
• Multiversality and Unnecessary Criticality in One Dimension
• Topological protection of Majorana polaritons in a cavity
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Entanglement in a second order topological insulator on a square lattice
• Correlations and entanglement in flat band models with variable Chern numbers
• Entanglement analysis of isotropic spin-1 chains
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Diagnosing Topological Edge States via Entanglement Monogamy
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States
• Entanglement spectrum and entropy in Floquet topological matter
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Topological Devil's staircase in atomic two-leg ladders
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Long-range entanglement and topological excitations
• Bipartite Fluctuations and Topology of Dirac and Weyl Systems
• Generalized Real-space Chern Number Formula and Entanglement Hamiltonian
• Entanglement and Majorana edge states in the Kitaev model
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Signature of Phase Transitions in the Disordered Quantum Spin Hall State From the Entanglement Spectrum
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Symmetry protected phases in inhomogeneous spin chains
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Detecting high-dimensional entanglement in cold-atom quantum simulators
• Nodal Line Entanglement Entropy: Generalized Widom Formula from Entanglement Hamiltonians
• Entanglement Driven Phase Transitions in Spin-Orbital Models
• Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
• Renormalization group approach to symmetry protected topological phases
• Topological chiral currents in the Gross-Neveu model extension
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Entanglement properties of Floquet Chern insulators
• Topological skyrmion phases of matter
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• On the relation of the entanglement spectrum to the bulk polarization
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• Density matrix renormalization group study in energy space for a single-impurity Anderson model and an impurity quantum phase transition
• Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases
• Critical Scaling Behaviors of Entanglement Spectra
• Comparative study of the density matrix embedding theory for the Hubbard models
• Protected Gapless Edge States In Trivial Topology
• Topological obstructed atomic limit by annihilating Dirac fermions
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian
• Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals
• Disorder-induced topology in quench dynamics
• Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
• Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches
• Entropic topological invariant for a gapped one-dimensional system
• Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
• Topological insulators with arbitrarily tunable entanglement
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
• Reentrance of Topological Phase in Spin-1 Frustrated Heisenberg Chain
• Tunable mode entanglement: topological Su-Schrieffer-Heeger (SSH) chain with an embedded Aharonov-Bohm quantum ring
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
• Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems
• Edge--Entanglement correspondence for gapped topological phases with symmetry
• New disordered anyon phase of doped graphene zigzag nanoribbon
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• Entanglement in 3D Kitaev Spin Liquids
• Bulk Entanglement Spectrum in Gapped Spin Ladders
• Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning
• Emergent universality in critical quantum spin chains: entanglement Virasoro algebra
• Can multipartite entanglement be characterized by two-point connected correlation functions ?
• Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic $J_1$-$J_1^{\prime }$-$J_2$ chain
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Symmetry classification of typical quantum entanglement
• Entanglement and particle fluctuations of one-dimensional chiral topological insulators
• Synthetic Hall tube of interacting fermions
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry
• BRST Symmetry: Boundary Conditions and Edge States in QED
• Entanglement entropy and entanglement spectrum of Bi${}_{1-x}$Sb${}_x$ (111) bilayers
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Characterization of helical states in semiconductor quantum wells using quantum information quantities
• Entanglement studies of interacting fermionic models
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Manifestations of topological band crossings in bulk entanglement spectrum: An analytical study for integer quantum Hall states
• Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Entanglement, subsystem particle numbers and topology in free fermion systems
• Properties of gapped systems in AdS/BCFT
• On integrable matrix product operators with bond dimension $D=4$
• Scaling of entanglement entropy at quantum critical points in random spin chains
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• From Hermitian critical to non-Hermitian point-gapped phases
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Numerical identification and gapped boundaries of abelian fermionic topological order
• Parity-dependent phase diagrams in spin-cluster two-leg ladders
• Partially topological phase in a quantum loop gas model with tension and pressure
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
• Classification of the anyon sectors of Kitaev's quantum double model
• Towards Entanglement Entropy of Random Large-N Theories
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Observable-enriched entanglement
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Threefold Way for Typical Entanglement
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain
• Tensor network states for the description of quantum many-body systems
• Entanglement entropy as a probe of topological phase transitions
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Mutual information in interacting spin systems
• Quantum cluster kink and ring frustration
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Phase Transition of Topological Index driven by Dephasing
• Symmetry-protected topological wire in a topological vacuum
• Phase Space Entanglement Spectrum
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Exact Mappings in Condensed Matter Physics
• Multipartite entanglement in quantum phase transitions
• The possible coexistence of superconductivity and topological electronic states in 1T-RhSeTe
• Non-local order parameters for fermion chains via the partial transpose
• Dynamical Geometry of the Haldane Model under a Quantum Quench
• Entanglement signatures of a percolating quantum system
• Entanglement spectrum of gapless topological phases: a case study with topological superconductors
• Entanglement Spectrum Resolved by Loop Symmetries