Topological edge modes and phase transition in the critical fermionic chain with long-range interaction

Abstract

The long-range interaction can fundamentally alter properties in gapped topological phases such as emergent massive edge modes. However, recent research has shifted attention to topological nontrivial critical points or phases, and it is natural to explore how long-range interaction influences them. In this work, we investigate the topological behavior and phase transition of extended Kitaev chains with long-range interactions, which can be derived from the critical Ising model via the Jordan-Wigner transformation in the short-range limit. Specifically, we analytically find the critical edge modes at the critical point remain stable against long-range interaction. More importantly, we observe these critical edge modes remain massless even when long-range interactions become substantially strong. As a byproduct, we numerically find that the critical behavior of the long-range model belongs to the free Majorana fermion universality class, which is entirely different from the long-range universality class in usual long-range spin models. Our work could shed new light on the interplay between long-range interactions (frustrated) and the gapless topological phases of matter.

arXiv comment13 pages, 11 figures. Any comments or suggestions are welcome !

References in corpus (94)

• Topological Insulators
• Topological insulators and superconductors
• Many-Body Physics with Ultracold Gases
• Quantum Computing
• Probing many-body dynamics on a 51-atom quantum simulator
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Cold atoms in cavity-generated dynamical optical potentials
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Zoo of quantum-topological phases of matter
• Topological phases of fermions in one dimension
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Hamiltonian Simulation by Qubitization
• Fidelity approach to quantum phase transitions
• Symmetry Protected Topological phases of Quantum Matter
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Quantum many-body models with cold atoms coupled to photonic crystals
• Topological superconducting phase in helical Shiba chains
• Digital quantum simulation of fermionic models with a superconducting circuit
• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Detection of Symmetry Protected Topological Phases in 1D
• Long-range interacting quantum systems
• Kitaev chains with long-range pairing
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Quantum Critical Scaling of Fidelity Susceptibility
• Choreographed entangle dances: topological states of quantum matter
• Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• Topology and edge modes in quantum critical chains
• Gapless topological phases and symmetry-enriched quantum criticality
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Statistical mechanics of the Cluster-Ising model
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Quantum phase transition between cluster and antiferromagnetic states
• Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Relations between Short Range and Long Range Ising models
• Topological Characterization of Extended Quantum Ising Models
• Long-range critical exponents near the short-range crossover
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Extended Kitaev chain with longer-range hopping and pairing
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Topological Luttinger Liquids from Decorated Domain Walls
• Entanglement area laws for long-range interacting systems
• Topological phases with long-range interactions
• The crossover region between long-range and short-range interactions for the critical exponents
• Critical exponents of O(N) models in fractional dimensions
• Topological Quantum Liquids with Long-Range Couplings
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Chiral Topological Superconductors Enhanced by Long-Range Interactions
• Information propagation and equilibration in long-range Kitaev chains
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain
• Pivot Hamiltonians as generators of symmetry and entanglement
• Entanglement entropy in the Long-Range Kitaev chain
• Gauging the Kitaev chain
• Floquet topological phase transitions in a periodically quenched dimer
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• One-dimensional quantum many body systems with long-range interactions
• Topological and symmetry-enriched random quantum critical points
• Edge states of the long-range Kitaev chain: an analytical study
• Decorated Defect Construction of Gapless-SPT States
• Emergent phase transition in Cluster Ising model with dissipation
• Universal entanglement spectrum in gapless symmetry protected topological states
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Building models of topological quantum criticality from pivot Hamiltonians
• Multi-critical topological transition at quantum criticality
• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Majorana flat band edge modes of topological gapless phase in 2D Kitaev square lattice
• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• Correlations, long-range entanglement and dynamics in long-range Kitaev chains
• Signatures of topological phase transition on a quantum critical line
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Quantum phase transition and critical behavior between the gapless topological phases
• Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
• Quantum phase transition between topologically distinct quantum critical points
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators

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• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
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• Phase diagram of the disordered Kitaev chain with long range pairing connected to external baths
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Gapless higher-order topology and corner states in Floquet systems
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• The global phase diagram of the cluster-XY spin chain with dissipation
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• 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
• Anomalous Dynamical Scaling at Topological Quantum Criticality