Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition

Abstract

We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasi-spins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from nonadiabatic to adiabatic regime. In the adiabatic regime, the quasi-spins trace the time dependent effective magnetic field and then oscillate between spin up and down states. While in the nonadiabatic regime, the quasi-spins cannot follow the time dependent effective magnetic field and feel an average magnetic field. We find the range of driving frequency over which the quasi-spins experience adiabatic cyclic processes. Moreover, we obtain the exact expression of the Loschmidt amplitude and generalized Loschmidt amplitude of the proposed Floquet system. The results represent that both pure and mixed states dynamical phase transition occurs when the system evolves adiabatically. In other words, the minimum required driving frequency for the appearance of Floquet DQPT is equal to the threshold frequency needed for transition from nonadiabatic to adiabatic regime.

arXiv commentTo appear in Phys. Rev. B

References in corpus (77)

• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Experimental realisation of the topological Haldane model
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Exploring the many-body localization transition in two dimensions
• Many-body localization in a quantum simulator with programmable random disorder
• On the phase structure of driven quantum systems
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Dynamical quantum phase transitions: a review
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Universal digital quantum simulation with trapped ions
• Equilibrium states of generic quantum systems subject to periodic driving
• Long-time behavior of periodically driven isolated interacting lattice systems
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Observation of the Meissner effect with ultracold atoms in bosonic ladders
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Observation of a dynamical topological phase transition
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Periodically driven ergodic and many-body localized quantum systems
• Pre-thermal phases of matter protected by time-translation symmetry
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Dynamical Topological Order Parameters far from Equilibrium
• Dynamical phase transitions after quenches in non-integrable models
• Quantum quench dynamics
• 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
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Boundary energy and boundary states in integrable quantum field theories
• Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• First order dynamical phase transitions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Dynamics after a sweep through a quantum critical point
• Dynamical quantum phase transitions in non-Hermitian lattices
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
• Observation of dynamical quantum phase transition by a superconducting qubit simulation
• Mixed state dynamical quantum phase transition and emergent topology
• Dynamical Topological Quantum Phase Transitions for Mixed States
• Quenches and dynamical phase transitions in a non-integrable quantum Ising model
• Floquet dynamical quantum phase transitions
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Phase Diagram of the spin S=1/2 Extended XY model
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• 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
• 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
• Measuring a Dynamical Topological Order Parameter in Quantum Walks
• Dynamical quantum phase transitions in discrete time crystals
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• Out-of-equilibrium phase diagram of long-range superconductors
• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Dynamical phase transitions, time-integrated observables and geometry of states
• The fate of dynamical phase transitions at finite temperatures and in open systems
• Dynamical quantum phase transitions and non-Markovian dynamics
• 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 transition in a system of non-interacting bosons
• Dynamical Topological Phase Transition in a Bose-Einstein Condensate
• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo
• Boundaries and unphysical fixed points in Dynamical Quantum Phase Transitions
• Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain
• Topological phases in adiabatic and nonadiabatic driven systems
• Signatures of topology in quantum quench dynamics and their interrelation
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points
• Quantum renormalization group approach to geometric phases in spin chains
• Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state

Cited by in corpus (51)

• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogs for Cosmological Analysis
• Floquet dynamical phase transition and entanglement spectrum
• Dynamical Topological Quantum Phase Transitions at Criticality
• Floquet dynamical quantum phase transitions under synchronized periodic driving
• Driving enhanced quantum sensing in partially accessible many-body systems
• Dissipative Floquet Dynamical Quantum Phase Transition
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Floquet topological phase transitions in a periodically quenched dimer
• Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Finite temperature dynamical quantum phase transition in a non-Hermitian system
• Engineering Floquet Dynamical Quantum Phase Transition
• Correlations and dynamical quantum phase transitions in an interacting topological insulator
• 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 a mesoscopic superconducting system
• Floquet dynamical quantum phase transitions in periodically quenched systems
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Loschmidt amplitude spectrum in dynamical quantum phase transitions
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Quantum spin fluctuations in dynamical quantum phase transitions
• 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
• Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model
• Detecting exceptional points through dynamics in non-Hermitian systems
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Dynamics of the Geometric Phase in Inhomogeneous Quantum Spin Chains
• Dynamical quantum phase transition in diamond: applications in quantum metrology
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Persistent anomaly in dynamical quantum phase transition in long-range non-Hermitian $p$-wave Kitaev chain
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Predicting topological quantum phase transition from dynamics via multisite entanglement
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice
• The Loschmidt Index
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Quantum coherence assisted dynamical phase transition
• Dynamical quantum phase transitions from random matrix theory
• Recognizing critical lines via entanglement in non-Hermitian systems
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
• 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