Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems

Abstract

We introduce the notion of a dynamical topological order parameter (DTOP) that characterises dynamical quantum phase transitions (DQPTs) occurring in the subsequent temporal evolution of "two dimensional" closed quantum systems, following a quench (or ramping) of a parameter of the Hamiltonian, {which generalizes the notion of DTOP introduced in Budich and Heyl, Phys. Rev. B 93, 085416 (2016) for one-dimensional situations}. This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur.

5 pages, 3 figures

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Topological characterization of periodically-driven quantum systems
• Topological classification of dynamical phase transitions
• Mixed-state fidelity and quantum criticality at finite temperature
• Observation of Lee-Yang zeros
• Decoherence induced by interacting quantum spin baths
• Topology induced anomalous defect production by crossing a quantum critical point
• First order dynamical phase transitions
• Large deviations and universality in quantum quenches
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Universal decoherence induced by an environmental quantum phase transition
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Fate of Majorana fermions and Chern numbers after a quantum quench
• Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
• Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence
• Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points
• Decoherence induced by a dynamic spin environment (I): The universal regime
• Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions

Cited by in corpus (58)

• Dynamical quantum phase transitions: a review
• Long-range interacting quantum systems
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Dynamical quantum phase transitions in non-Hermitian lattices
• Mixed state dynamical quantum phase transition and emergent topology
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Floquet dynamical phase transition and entanglement spectrum
• Dynamical quantum phase transitions: a brief survey
• Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
• Dynamical quantum phase transitions in discrete time crystals
• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Out-of-equilibrium phase diagram of long-range superconductors
• Dynamical Topological Quantum Phase Transitions at Criticality
• Floquet dynamical quantum phase transitions under synchronized periodic driving
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants
• Dynamical and excited-state quantum phase transitions in collective systems
• One-dimensional quantum many body systems with long-range interactions
• Engineering Floquet Dynamical Quantum Phase Transition
• Dynamical quantum phase transition for mixed states in open systems
• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Dynamical topological invariants and reduced rate functions for dynamical quantum phase transitions in two dimensions
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Driven quantum many-body systems and out-of-equilibrium topology
• Nonanalyticity of circuit complexity across topological phase transitions
• Zeros of Loschmidt echo in the presence of Anderson localization
• Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain
• Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Entanglement and precession in two-dimensional dynamical quantum phase transitions
• Effects of the Dzyaloshinsky-Moriya interaction on nonequilibrium thermodynamics in the $XY$ chain in a transverse field
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Dissipative preparation of many-body Floquet Chern insulators
• Dynamical quantum phase transitions in Weyl semimetals
• Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain
• Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points
• Dynamical quantum phase transitions following a noisy quench
• Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids
• Dynamics of edge current in a linearly quenched Haldane model
• Metamorphic dynamical quantum phase transition in double-quench processes at finite temperatures
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Geometrical quench and dynamical quantum phase transition in the $\alpha -T_3$ lattice
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Dynamical quantum phase transitions in Stark quantum spin chains
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Probing quantum phase transition via quantum speed limit
• Topological Classification of Dynamical Quantum Phase Transitions in the 1D XY model via Critical Mode Analysis
• Floquet dynamical quantum phase transitions in periodically flux-quenched systems
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench