Entanglement transitions in a periodically driven non-Hermitian Ising chain

Abstract

We study entanglement transitions in a periodically driven Ising chain in the presence of an imaginary transverse field $\gamma$ as a function of drive frequency ${\omega }_D$. In the high drive amplitude and frequency regime, we find a critical value $\gamma ={\gamma }_c$ below which the steady state half-chain entanglement entropy, $S_{L/2}$, scales with chain length $L$ as $S_{L/2}\sim \ln L$; in contrast, for $\gamma >{\gamma }_c$, it becomes independent of $L$. In the small $\gamma$ limit, we compute the coefficient, $\alpha$, of the $\ln L$ term analytically using a Floquet perturbation theory and trace its origin to the presence of Fisher-Hartwig jump singularities in the correlation function of the driven chain. We also study the frequency dependence of ${\gamma }_c$ and show that ${\gamma }_c\to 0$ at special drive frequencies; at these frequencies, which we analytically compute, $S_{L/2}$ remain independent of $L$ for all $\gamma$. This behavior can be traced to an approximate emergent symmetry of the Floquet Hamiltonian at these drive frequencies which we identify. Finally, we discus the behavior of the driven system at low and intermediate drive frequencies. Our analysis shows the presence of volume law behavior of the entanglement in this regime $S_{\ell }\sim \ell$ for small subsystem length $\ell \le {\ell }^{\ast }({\omega }_D)$. We identify ${\ell }^{\ast }({\omega }_D)$ and tie its existence to the effective long-range nature of the Floquet Hamiltonian of the driven chain for small subsystem size. We discuss the applicability of our results to other integrable non-hermitian models.

arXiv commentv2; 8 figs 17 pages; minor changes

References in corpus (168)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Edge states and topological invariants of non-Hermitian systems
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Photovoltaic Hall effect in graphene
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• The Magnus expansion and some of its applications
• Observation of a Discrete Time Crystal
• Calculation of reduced density matrices from correlation functions
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• An Area Law for One Dimensional Quantum Systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Floquet Time Crystals
• Lasing in topological edge states of a 1D lattice
• Non-Hermitian Chern bands
• On the phase structure of driven quantum systems
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum trajectories and open many-body quantum systems
• Effective quantum spin systems with ion traps
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Anatomy of skin modes and topology in non-Hermitian systems
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
• Reduced density matrices and entanglement entropy in free lattice models
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamical quantum phase transitions: a review
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• Observation of parity-time symmetry breaking in a single spin system
• Topological Hybrid Silicon Microlasers
• Non-Hermitian topological phenomena: A review
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Topological singularities and the general classification of Floquet-Bloch systems
• Non-Hermitian Delocalization and Eigenfunctions
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Parity-time-symmetric quantum critical phenomena
• Entanglement in XY Spin Chain
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Majorana bound states from exceptional points in non-topological superconductors
• Floquet generation of Majorana end modes and topological invariants
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Atomic three-body loss as a dynamical three-body interaction
• Many-body energy localization transition in periodically driven systems
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Effective Theory of Floquet Topological Transitions
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Heralded magnetism in non-Hermitian atomic systems
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Parity-time-symmetric topological superconductor
• Entanglement renormalization, scale invariance, and quantum criticality
• Exotic Freezing of Response in Quantum Many-Body System
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Collapse and revival of quantum many-body scars via Floquet engineering
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Topological non-Hermitian origin of surface Maxwell waves
• Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators
• Dynamical quantum phase transitions in non-Hermitian lattices
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Hall Conductance of a Non-Hermitian Chern Insulator
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Topological classification of non-Hermitian systems with reflection symmetry
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• Many-body topology of non-Hermitian systems
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Floquet dynamical quantum phase transitions
• Edge states at the interface of non-Hermitian systems
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Many-body approach to non-Hermitian physics in fermionic systems
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Surface and 3D quantum Hall effects from engineering of exceptional points in nodal-line semimetals
• Kondo effect in a parity-time-symmetric non-Hermitian Hamiltonian
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Dynamical localization in a chain of hard core bosons under a periodic driving
• Floquet dynamical phase transition and entanglement spectrum
• Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation
• Topological phases in Kitaev chain with imbalanced pairing
• Majorana edge modes in the Kitaev model
• Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Topological protection from exceptional points in Weyl and nodal line semimetals
• Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
• Absence of dynamical localization in interacting driven systems
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• High order exceptional points in ultracold Bose gases
• Effects of interactions on periodically driven dynamically localized systems
• Dual topological characterization of non-Hermitian Floquet phases
• Effects of periodic kicking on dispersion and wave packet dynamics in graphene
• Dynamic freezing of strongly correlated ultracold bosons
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Dynamic winding number for exploring band topology
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Controlling quantum critical dynamics of isolated systems
• Exceptional odd-frequency pairing in non-Hermitian superconducting systems
• Symmetry and topological classification of Floquet non-Hermitian systems
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Stable topological edge states in a non-Hermitian four-band model
• Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Periodically driven integrable systems with long-range pair potentials
• Topological phase transition measured in a dissipative metamaterial
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Signatures and conditions for phase band crossings in periodically driven integrable systems
• (Quasi)Periodic revivals in periodically driven interacting quantum systems
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Topology of multipartite non-Hermitian one-dimensional systems
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• Spontaneously Broken Particle-Hole Symmetry in Photonic Graphene with Gain and Loss
• Prethermal fragmentation in a periodically driven Fermionic chain
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Periodically driven Rydberg chains with staggered detuning
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Dynamical Transition for a class of integrable models coupled to a bath
• Topological superconductivity enhanced by exceptional points
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach
• Exceptional dynamics of interacting spin liquids
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems

Cited by in corpus (9)

• Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain
• Disappearance of measurement-induced phase transition in a quantum spin system for large sizes