Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension

Abstract

Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.

12 pages, 8 figures. Accepted version

References in corpus (75)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Entanglement in quantum critical phenomena
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Liquid States
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Calculation of reduced density matrices from correlation functions
• Quantum Spin Liquids
• Topological orders and Edge excitations in FQH states
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Zoo of quantum-topological phases of matter
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Symmetry Protected Topological phases of Quantum Matter
• 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
• Detection of Symmetry Protected Topological Phases in 1D
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Entanglement entropy and entanglement spectrum of the Kitaev model
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Choreographed entangle dances: topological states of quantum matter
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Gapless topological phases and symmetry-enriched quantum criticality
• Topology and edge modes in quantum critical chains
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Statistical mechanics of the Cluster-Ising model
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Quantum phase transition between cluster and antiferromagnetic states
• How universal is the entanglement spectrum?
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Majorana Edge States in Interacting Two-chain Ladders of Fermions
• Topological Luttinger Liquids from Decorated Domain Walls
• Exploring Large-Scale Entanglement in Quantum Simulation
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Topological degeneracy and pairing in a one-dimensional gas of spinless Fermions
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Gauging the Kitaev chain
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Floquet topological phase transitions in a periodically quenched dimer
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Topological and symmetry-enriched random quantum critical points
• Emergent phase transition in Cluster Ising model with dissipation
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• Decorated Defect Construction of Gapless-SPT States
• Topological holography, quantum criticality, and boundary states
• Universal entanglement spectrum in gapless symmetry protected topological states
• Entanglement Spectrum of Su-Schrieffer-Heeger-Hubbard Model
• From one-dimensional charge conserving superconductors to the gapless Haldane phase
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Topological edge modes without symmetry in quasiperiodically driven spin chains
• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• 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
• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• Entanglement spectrum and entropy in Floquet topological matter
• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• The global phase diagram of the cluster-XY spin chain with dissipation
• Quantum $z=2$ Lifshitz criticality in one-dimensional interacting fermions

Cited by in corpus (7)

• Deconfined criticality as intrinsically gapless topological state in one dimension
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Topologically nontrivial multicritical points
• Entanglement dynamics in minimal Kitaev chains
• Entanglement spectrum of gapless topological phases: a case study with topological superconductors
• Anomalous Dynamical Scaling at Topological Quantum Criticality