Emergent conservation in Floquet dynamics of integrable non-Hermitian models

Abstract

We study the dynamics of a class of integrable non-Hermitian free-fermionic models driven periodically using a continuous drive protocol characterized by an amplitude $g_1$ and frequency ${\omega }_D$. We derive an analytic, albeit perturbative, Floquet Hamiltonian for describing such systems using Floquet perturbation theory with $g_1^{-1}$ being the perturbation parameter. Our analysis indicates the existence of special drive frequencies at which an approximately conserved quantity emerges. The presence of such an almost conserved quantity is reflected in the dynamics of the fidelity, the correlation functions and the half-chain entanglement entropy of the driven system. In addition, it also controls the nature of the steady state of the system. We show that one-dimensional (1D) transverse field Ising model, with an imaginary component of the transverse field, serves as an experimentally relevant example of this phenomenon. In this case, the transverse magnetization is approximately conserved; this conservation leads to complete suppression of oscillatory features in the transient dynamics of fidelity, magnetization, and entanglement of the driven chain at special drive frequencies. We discuss the nature of the steady state of the Ising chain near and away from these special frequencies, demonstrate the protocol independence of this phenomenon by showing its existence for discrete drive protocols, and suggest experiments which can test our theory.

14 pages, 7 figs; v2 with minor changes and added refs

References in corpus (40)

• The electronic properties of graphene
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• The Magnus expansion and some of its applications
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum trajectories and open many-body quantum systems
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological Transition in a Non-Hermitian Quantum Walk
• Observation of parity-time symmetry breaking in a single spin system
• Non-Hermitian topological phenomena: A review
• Effective Theory of Floquet Topological Transitions
• Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Topological non-Hermitian origin of surface Maxwell waves
• Many-body topology of non-Hermitian systems
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Absence of dynamical localization in interacting driven systems
• Effects of interactions on periodically driven dynamically localized systems
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Controlling quantum critical dynamics of isolated systems
• Symmetry and topological classification of Floquet non-Hermitian systems
• Geometric Heat Flux for Classical Thermal Transport in Interacting Open Systems
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• (Quasi)Periodic revivals in periodically driven interacting quantum systems
• Topology of multipartite non-Hermitian one-dimensional systems
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Periodically driven Rydberg chains with staggered detuning
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Standing Sausage Perturbations in solar coronal loops with diffuse boundaries: An initial-value-problem perspective
• Observation of Geometric Heat Pump Effect in Periodic Driven Thermal Diffusion
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices

Cited by in corpus (11)

• Non-Hermitian Floquet Topological Matter -- A Review
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Arresting Quantum Chaos Dynamically in Transmon Arrays
• Extended unitarity and absence of skin effect in periodically driven systems
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain