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.

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

References in corpus (24)

• Many-Body Physics with Ultracold Gases
• Quantum Computing
• Probing many-body dynamics on a 51-atom quantum simulator
• Cold atoms in cavity-generated dynamical optical potentials
• Digital quantum simulation of fermionic models with a superconducting circuit
• Kitaev chains with long-range pairing
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Choreographed entangle dances: topological states of quantum matter
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Critical exponents of O(N) models in fractional dimensions
• The crossover region between long-range and short-range interactions for the critical exponents
• Chiral Topological Superconductors Enhanced by Long-Range Interactions
• Edge states of the long-range Kitaev chain: an analytical study
• Emergent phase transition in Cluster Ising model with dissipation
• Universal entanglement spectrum in gapless symmetry protected topological states
• Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators
• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• 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
• Quantum phase transition between topologically distinct quantum critical points
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators

Cited by in corpus (16)

• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Topological edge states at Floquet quantum criticality
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• 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