Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems

Abstract

Topological phenomena in quantum critical systems have recently attracted growing attention, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, a general framework for identifying such nontrivial phenomena, particularly in higher-dimensional systems, remains insufficiently explored. In this work, we propose a universal fingerprint for detecting nontrivial topology in critical free-fermion systems protected by global on-site symmetries. Specifically, we analytically establish an exact relation between the bulk entanglement spectrum and the boundary energy spectrum at topological criticality in arbitrary dimensions, demonstrating that the degeneracy of edge modes can be extracted from the bulk entanglement spectrum. These findings, further supported by numerical simulations of lattice models, provide a universal fingerprint for identifying nontrivial topology in critical free-fermion systems.

References in corpus (81)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Weyl and Dirac Semimetals in Three Dimensional Solids
• The density-matrix renormalization group in the age of matrix product states
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological Materials: Weyl Semimetals
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• The ITensor Software Library for Tensor Network Calculations
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Zoo of quantum-topological phases of matter
• Topological phases of fermions in one dimension
• Reduced density matrices and entanglement entropy in free lattice models
• Symmetry Protected Topological phases of Quantum Matter
• The effects of interactions on the topological classification of free fermion systems
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum of topological insulators and superconductors
• Entanglement entropy of random quantum critical points in one dimension
• Electrical switching of magnetic order in an orbital Chern insulator
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Density-Matrix Spectra of Solvable Fermionic Systems
• Entanglement hamiltonians in two-dimensional conformal field theory
• Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• The entanglement gap and a new principle of adiabatic continuity
• Bulk-Edge Correspondence in the Entanglement Spectra
• Observation of high-temperature quantum anomalous Hall regime in intrinsic MnBi${}_2$Te${}_4$/Bi${}_2$Te${}_3$ superlattice
• Gapless topological phases and symmetry-enriched quantum criticality
• Topology and edge modes in quantum critical chains
• Intrinsically Gapless Topological Phases
• Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries
• Gapless Symmetry Protected Topological Order
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Topological Entanglement and Clustering of Jain Hierarchy States
• Physics at the entangling surface
• How universal is the entanglement spectrum?
• Topological Luttinger Liquids from Decorated Domain Walls
• Exploring Large-Scale Entanglement in Quantum Simulation
• Non-Invertible Duality Transformation Between SPT and SSB Phases
• Symmetric Mass Generation
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• Interaction effects on 1D fermionic symmetry protected topological phases
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Pivot Hamiltonians as generators of symmetry and entanglement
• Gauging the Kitaev chain
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Topological and symmetry-enriched random quantum critical points
• Decorated Defect Construction of Gapless-SPT States
• Topological holography, quantum criticality, and boundary states
• Universal entanglement spectrum in gapless symmetry protected topological states
• Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators
• Measuring entanglement entropy and its topological signature for phononic systems
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• Building models of topological quantum criticality from pivot Hamiltonians
• Quantum phase transition and critical behavior between the gapless topological phases
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Quantum phase transition between topologically distinct quantum critical points
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Symmetry-Enriched Criticality in a Coupled Spin-Ladder
• Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Topological edge states at Floquet quantum criticality
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Topological quantum criticality from multiplicative topological phases
• Topological physics in quantum critical systems
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Bipartite entanglement and surface criticality: The extra contribution of non-ordinary edge in entanglement
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum

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