Topology of one dimensional quantum systems out of equilibrium

Abstract

We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the time-dependent wavefunction -- a phenomenon which we dub "dynamically-induced symmetry breaking". This leads to the possibility of a time-varying bulk index after quenching within non-interacting gapped topological phases. The consequences are observable experimentally through particle transport measurements. With reference to the entanglement spectrum, we explain how the topology of the wavefunction can change out of equilibrium, both for non-interacting fermions and for symmetry-protected topological phases protected by antiunitary symmetries.

arXiv comment5+5 pages, 1 figure, 1 table. Accepted for publication in PRL

References in corpus (44)

• Topological Insulators
• Topological insulators and superconductors
• Unpaired Majorana fermions in quantum wires
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological characterization of periodically-driven quantum systems
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• 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
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Entanglement spectrum of topological insulators and superconductors
• Observation of a dynamical topological phase transition
• Periodic Table for Floquet Topological Insulators
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Dynamical Topological Order Parameters far from Equilibrium
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Dynamical preparation of Floquet Chern insulators
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Quantum Quenches in Chern Insulators
• Tomography of band insulators from quench dynamics
• Topological phases: Classification of topological insulators and superconductors of non-interacting Fermions, and beyond
• Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
• Dynamical topological invariant after a quantum quench
• Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
• Fate of Majorana fermions and Chern numbers after a quantum quench
• Emergent eigenstate solution to quantum dynamics far from equilibrium
• Hall Response and Edge Current Dynamics in Chern Insulators out of Equilibrium
• Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons
• Topological Blocking in Quantum Quench Dynamics
• Non-equilibrium Fractional Hall Response After a Topological Quench
• Realizing and detecting a topological insulator in the AIII symmetry class
• Out-of-equilibrium dynamics and thermalization of string order
• Entanglement properties of the time periodic Kitaev Chain
• Destruction of string order after a quantum quench
• Topological indexes in symmetry preserving dynamics

Cited by in corpus (66)

• Non-Hermitian Physics
• Topological Bands for Ultracold Atoms
• Tenfold Way for Quadratic Lindbladians
• Measuring topology by dynamics: Chern number from linking number
• Realization of ideal Weyl semimetal band in ultracold quantum gas with 3D Spin-Orbit coupling
• Many-body topological invariants from randomized measurements
• Symmetry classes of open fermionic quantum matter
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Topological Marker Currents in Chern Insulators
• Classification of topological insulators and superconductors out of equilibrium
• Post-Quench Evolution of Complexity and Entanglement in a Topological System
• Type-II quadrupole topological insulators
• Characterizing topological phases by quantum quenches: A general theory
• Dynamical topological quantum phase transitions in nonintegrable models
• Classification of Matrix-Product Unitaries with Symmetries
• Kibble-Zurek behavior in disordered Chern insulators
• Driven quantum many-body systems and out-of-equilibrium topology
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• Stability of Time-Reversal Symmetry Protected Topological Phases
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Signatures of topology in quantum quench dynamics and their interrelation
• Cooper-pair transistor as a minimal topological quantum circuit
• Quench Dynamics and Hall Response of Interacting Chern Insulators
• Dissipative preparation of many-body Floquet Chern insulators
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Chern number and Berry curvature for Gaussian mixed states of fermions
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
• Competing Orders and Unconventional Criticality in the Su-Schrieffer-Heeger Model
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Linking invariant for the quench dynamics of a two-dimensional two-band Chern insulator
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven SSH chain
• Dynamical preparation of a topological state and out of equilibrium bulk boundary correspondence in a SSH chain under periodic driving
• Edge modes and symmetry-protected topological states in open quantum systems
• Long-range entanglement and topological excitations
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Emergent topology and symmetry-breaking order in correlated quench dynamics
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Correlation-Assisted Quantized Charge Pumping
• Disorder-induced topology in quench dynamics
• Observation of dynamical topology in 1D
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Interaction quench and thermalization in a one-dimensional topological Kondo insulator
• Excitonic Tonks-Girardeau and charge-density wave phases in monolayer semiconductors
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Geometric phases of Topological Systems under Quench Process
• Time-reversal invariant topological skyrmion phases
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading
• Topology in the space-time scaling limit of quantum dynamics
• Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion
• Time-dependent driving and topological protection in the fractional Josephson effect
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Dynamical signatures of symmetry protected topology following symmetry breaking
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• Emergence of topological states in relaxation dynamics of interacting bosons
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Non-adiabatic dynamics of the entanglement entropy in a symmetry-breaking Haldane insulator
• Evolution of density variations in a trapped atomic superfluid driven into turbulence
• Finite-rate quench in disordered Chern and $Z_2$ topological insulators
• Ultracold atomic lattice systems for simulating topological phases: A review