Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

Abstract

We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to unit cells containing many atoms but with the same symmetry properties. Such models have a richer structure of dynamical quantum phase transitions than the simple two-band topological insulator models typically considered previously, with both quasiperiodic and aperiodic dynamical quantum phase transitions present. Moreover the aperiodic transitions can still occur for quenches within a single topological phase. We also investigate the boundary contributions from the presence of the topologically protected edge states of this model. Plateaus in the boundary return rate are related to the topology of the time evolving Hamiltonian, and hence to a dynamical bulk-boundary correspondence. We go on to consider the dynamics of the entanglement entropy generated after a quench, and its potential relation to the critical times of the dynamical quantum phase transitions. Finally, we investigate the fidelity susceptibility as an indicator of the topological phase transitions, and find a simple scaling law as a function of the number of bands of our multiband model which is found to be the same for both bulk and boundary fidelity susceptibilities.

14 pages, 20 figures

References in corpus (76)

• Topological Insulators
• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Calculation of reduced density matrices from correlation functions
• Topological Bands for Ultracold Atoms
• Electron Counting Statistics and Coherent States of Electric Current
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Ground state overlap and quantum phase transitions
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Quantum Quench in the Transverse Field Ising Chain
• Dynamical quantum phase transitions: a review
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Topological classification of dynamical phase transitions
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Mixed-state fidelity and quantum criticality at finite temperature
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Decoherence induced by interacting quantum spin baths
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Entanglement entropy and the Berry phase in solid states
• Strong Quantum Nonlocality without Entanglement
• Ground-state fidelity in one-dimensional gapless model
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Long-distance entanglement and quantum teleportation in XX spin chains
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Qubit Teleportation and Transfer across Antiferromagnetic Spin Chains
• Quantum fidelity in the thermodynamic limit
• Mixed state dynamical quantum phase transition and emergent topology
• Dynamical Topological Quantum Phase Transitions for Mixed States
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Observation of a Transition Between Dynamical Phases in a Quantum Degenerate Fermi Gas
• Floquet dynamical quantum phase transitions
• Loschmidt Echo Revivals: Critical and Noncritical
• Dynamical Quantum Phase Transitions: A Geometric Picture
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Fidelity analysis of topological quantum phase transitions
• Dynamical topological transitions in the massive Schwinger model with a θ-term
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• A bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors
• Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
• Dynamical quantum phase transitions in $U(1)$ quantum link models
• Observation of dynamical phase transitions in a topological nanomechanical system
• Locality and thermalization in closed quantum systems
• The fate of dynamical phase transitions at finite temperatures and in open systems
• Loschmidt echo and dynamical fidelity in periodically driven quantum systems
• Dynamical quantum phase transitions in the quantum Potts chain
• Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model
• Dynamical Topological Phase Transition in a Bose-Einstein Condensate
• Dynamical quantum phase transition in a system of non-interacting bosons
• Universality in dynamical phase transitions of diffusive systems
• Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field
• Dynamical topological quantum phase transitions in nonintegrable models
• Decoherence from spin environments: Loschmidt echo and quasiparticle excitations
• Boundaries and unphysical fixed points in Dynamical Quantum Phase Transitions
• Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems
• Exact results on the quench dynamics of the entanglement entropy in the toric code
• Quenching in Chern insulators with satellite Dirac points: The fate of edge states
• Dynamical quantum phase transitions in the random field Ising model
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Closed and Open System Dynamics in a Fermionic Chain with a Microscopically Specified Bath: Relaxation and Thermalization
• Dynamical Phase Transitions in Topological Insulators
• Disentangling Sources of Quantum Entanglement in Quench Dynamics
• Fidelity in topological superconductors with end Majorana fermions

Cited by in corpus (31)

• Floquet dynamical phase transition and entanglement spectrum
• Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
• Dynamical Topological Quantum Phase Transitions at Criticality
• Dissipative Floquet Dynamical Quantum Phase Transition
• Engineering Floquet Dynamical Quantum Phase Transition
• Topological dynamical quantum phase transition in a quantum skyrmion phase
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Floquet dynamical quantum phase transitions in periodically quenched systems
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Topology of critical chiral phases: multiband insulators and superconductors
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Complex dynamics approach to dynamical quantum phase transitions: the Potts model
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Geometrical quench and dynamical quantum phase transition in the $\alpha -T_3$ lattice
• Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy
• Quantum coherence assisted dynamical phase transition
• Amplifying quantum correlations with quench dynamics in a quantum spin chain: Steady-states versus ground-states
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Topological Classification of Dynamical Quantum Phase Transitions in the 1D XY model via Critical Mode Analysis
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Entanglement entropy as a probe of topological phase transitions