Characterization of topological phase transitions via topological properties of transition points

Abstract

We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of momentum and transition driving parameter. By applying our scheme to the Su-Schrieffer-Heeger model and Haldane model, we demonstrate that the topological phase transition can be well characterized by the defined topological invariant of the transition point, which reflects the change of topological invariants of topologically different phases across the phase transition point.

6 pages, 5 figures

References in corpus (10)

• Classification of topological insulators and superconductors in three spatial dimensions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Geometric phases and criticality in spin chain systems
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Topology induced anomalous defect production by crossing a quantum critical point
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Abelian and Non-Abelian Quantum Geometric Tensor
• Virtual Topological Insulators with Real Quantized Physics
• Hidden-symmetry-protected topological phases on a one-dimensional lattice

Cited by in corpus (36)

• Geometry of quantum phase transitions
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Dynamical topological invariant after a quantum quench
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Topology and interactions in the photonic Creutz and Creutz-Hubbard ladders
• The Charging Performance of Su-Schrieffer-Heeger Quantum Battery
• Winding numbers of phase transition points for one-dimensional topological systems
• Quantum Charge Pumps with Topological Phases in Creutz Ladder
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems
• Fast quantum transfer mediated by topological domain walls
• Quantum walks in commensurate off-diagonal Aubry-André-Harper model
• Majorana charges, winding numbers and Chern numbers in quantum Ising models
• Topological invariants for phase transition points of one-dimensional ${\mathbb{Z}}_2$ topological systems
• Topological insulating phases from two-dimensional nodal loop semimetals
• Topological properties of a generalized spin-orbit-coupled Su-Schrieffer-Heeger model
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Topological properties of non-Hermitian Creutz Ladders
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Chiral topological insulating phases from three-dimensional nodal loop semimetals
• Multicriticality in a one-dimensional topological band insulator
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Topological properties of a periodically driven Creutz ladder
• Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube
• Quantum mold casting for topological insulating and edge states
• Transition from degeneracy to coalescence: theorem and applications
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Topological Phase Transition of A Non-Hermitian Crosslinked Chain
• Quantum phase transition induced by real-space topology
• Parallel dynamics between non-Hermitian and Hermitian systems
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Higher order topology in a Creutz ladder
• Entanglement entropy as a probe of topological phase transitions
• Periodic dynamics in an Ising chain with a quadratic transverse field