Mixed state dynamical quantum phase transition and emergent topology

Abstract

Preparing an integrable system in a mixed state described by a thermal density matrix , we subject it to a sudden quench and explore the subsequent unitary dynamics. Defining a version of the generalised Loschmidt overlap amplitude (GLOA) through the purifications of the time evolved density matrix, we claim that non-analyiticies in the corresponding "dynamical free energy density" persist and is referred to as mixed state dynamical quantum phase transitions (MSDQPTs). Furthermore, these MSDQPTs are uniquely characterised by a topological index constructed by the application of the Pancharatnam geometry on the purifications of the thermal density matrix; the quantization of this index however persists up to a critical temperature. These claims are corroborated analysing the non-equilibrium dynamics of a transverse Ising chain initially prepared in a thermal state and subjected to a sudden quench of the transverse field.

5 pages, 3 figures and supplementary material

References in corpus (89)

• Many-Body Physics with Ultracold Gases
• Photonic Floquet Topological Insulators
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Experimental realisation of the topological Haldane model
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• The many-body localization phase transition
• Photovoltaic Hall effect in graphene
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Quantum many-body systems out of equilibrium
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Time-dependence of correlation functions following a quantum quench
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Light-cone-like spreading of correlations in a quantum many-body system
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Quantum Quenches in Extended Systems
• Geometric phases for mixed states in interferometry
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Floquet generation of Majorana end modes and topological invariants
• Dynamical Topological Order Parameters far from Equilibrium
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions: scaling and universality
• 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
• Dynamical phase diagram of spin chains with long-range interactions
• Periodic steady state and interference in a periodically driven quantum system
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
• Topology induced anomalous defect production by crossing a quantum critical point
• Exotic Freezing of Response in Quantum Many-Body System
• Quantum Quenches in Chern Insulators
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Emergent thermodynamics in a quenched quantum many-body system
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• First order dynamical phase transitions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Dynamics after a sweep through a quantum critical point
• Large deviations and universality in quantum quenches
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Dynamical Topological Quantum Phase Transitions for Mixed States
• Unitary equilibrations: probability distribution of the Loschmidt echo
• Quenches and dynamical phase transitions in a non-integrable quantum Ising model
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Topological indices for open and thermal systems via Uhlmann's phase
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Universal decoherence induced by an environmental quantum phase transition
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid
• Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Work distribution and edge singularities for generic time-dependent protocols in extended systems
• Fate of Majorana fermions and Chern numbers after a quantum quench
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
• Loschmidt echo and dynamical fidelity in periodically driven quantum systems
• Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model
• Survival probability of an edge Majorana in a 1-D p-wave superconducting chain under sudden quenching of parameters
• Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points
• Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence
• Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons
• Decoherence induced by a dynamic spin environment (I): The universal regime
• Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems
• Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment
• Asymptotic work statistics of periodically driven Ising chains
• Finite time interaction quench in a Luttinger model
• Dynamics of decoherence: universal scaling of the decoherence factor
• Signature of a Continuous Quantum Phase Transition in Nonequilibrium Energy Absorption: Footprints of Criticality on Highly Excited States
• Locating topological phase transitions using nonequilibrium signatures in local bulk observables
• Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions
• One and two-dimensional quantum models: quenches and the scaling of irreversible entropy
• Sudden jumps and plateaus in the quench dynamics of a Bloch state
• Dynamical quantum phase transitions

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• Dynamical quantum phase transitions: a review
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• Dynamical quantum phase transitions in non-Hermitian lattices
• Dynamical Topological Quantum Phase Transitions for Mixed States
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• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• 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 phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
• Dynamical quantum phase transitions in discrete time crystals
• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Dynamical quantum phase transitions in $U(1)$ quantum link models
• Observation of dynamical phase transitions in a topological nanomechanical system
• Dynamical Topological Quantum Phase Transitions at Criticality
• Floquet dynamical quantum phase transitions under synchronized periodic driving
• The fate of dynamical phase transitions at finite temperatures and in open systems
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Dissipative Floquet Dynamical Quantum Phase Transition
• Local measures of dynamical quantum phase transitions
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Dynamical quantum phase transition from a critical quantum quench
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Dynamical quantum phase transitions and non-Markovian dynamics
• Finite temperature dynamical quantum phase transition in a non-Hermitian system
• Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian 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
• Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases
• Many-body dynamical phase transition in quasi-periodic potential
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Driven quantum many-body systems and out-of-equilibrium topology
• Controlling Dynamical Quantum Phase Transitions
• Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath
• Signatures of topology in quantum quench dynamics and their interrelation
• Topological phase transitions at finite temperature
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Effects of the Dzyaloshinsky-Moriya interaction on nonequilibrium thermodynamics in the $XY$ chain in a transverse field
• Dissipative preparation of many-body Floquet Chern insulators
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Dynamical quantum phase transitions in Weyl semimetals
• Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Dynamical quantum phase transitions following a noisy quench
• Lindblad master equation approach to the dissipative quench dynamics of planar superconductors
• Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids
• Dissipation driven dynamical topological phase transitions in two-dimensional superconductors
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Dynamics of edge current in a linearly quenched Haldane model
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature
• Dynamical relaxation behaviors of a critical quench
• Metamorphic dynamical quantum phase transition in double-quench processes at finite temperatures
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Persistent anomaly in dynamical quantum phase transition in long-range non-Hermitian $p$-wave Kitaev chain
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Speeding up Pontus-Mpemba effects via dynamical phase transitions
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Reconstructing Thermal Quantum Quench Dynamics from Pure States
• 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
• Tunneling phase diagrams in anisotropic Multi-Weyl semimetals
• Quantum coherence assisted dynamical phase transition
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Singularities in the Loschmidt echo of quenched topological superconductors
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Speedup of thermodynamic entropy production via quantum dynamical criticality
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit
• Superconducting phase in the BCS model with imaginary magnetic field. III. Non-vanishing free dispersion relations
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model
• Topological Classification of Dynamical Quantum Phase Transitions in the 1D XY model via Critical Mode Analysis
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Asymmetry and dynamical criticality
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Dynamical Quantum Phase Transitions in Interacting Atomic Interferometers
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems