Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models

Abstract

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse ($g$) and longitudinal ($h$) magnetic fields. This model exhibits a continuous quantum transition (CQT) at $g=g_c$ and $h=0$, and first-order quantum transitions (FOQTs) driven by $h$ along the line $h=0$ ($g<g_c$). In the integrable limit $h=0$, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value $h_i<0$ to a positive value $h_f>0$. We focus on values of $h_f$ such that the spectrum of the post-QQ Hamiltonian $H(g,h_f)$ lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of $g$, finding qualitatively distinct behaviors for $g>g_c$ (where the chain is in the disordered phase), for $g=g_c$ (QQ across the CQT), and for $g<g_c$ (QQ across the FOQT line).

25 pages, some comments and refs added

References in corpus (115)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• 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
• Localization of interacting fermions at high temperature
• Critical Phenomena and Renormalization-Group Theory
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Relaxation and Pre-thermalization in an Isolated Quantum System
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many body localization in Heisenberg XXZ magnet in a random field
• Light-cone-like spreading of correlations in a quantum many-body system
• Dynamics of a Quantum Phase Transition
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Demonstration of a small programmable quantum computer with atomic qubits
• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Dynamical quantum phase transitions: a review
• Quantum Entanglement Growth Under Random Unitary Dynamics
• The Statistical Theory of Quantum Dots
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Time evolution of local observables after quenching to an integrable model
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Computational Studies of Quantum Spin Systems
• Dynamic transitions and hysteresis
• Digitized adiabatic quantum computing with a superconducting circuit
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Quantum quenches in 1+1 dimensional conformal field theories
• Strong and weak thermalization of infinite non-integrable quantum systems
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Real time confinement following a quantum quench to a non-integrable model
• Entanglement Entropy dynamics in Heisenberg chains
• Quasilocal charges in integrable lattice systems
• Alternatives to Eigenstate Thermalization
• Strongly correlated fermions after a quantum quench
• Ageing Properties of Critical Systems
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Prethermalization and universal dynamics in near-integrable quantum systems
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Conformal field theory out of equilibrium: a review
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators
• First order phase transition in the Quantum Adiabatic Algorithm
• Entropy of isolated quantum systems after a quench
• Prethermalization and Thermalization in Isolated Quantum Systems
• Large deviations and universality in quantum quenches
• Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
• Semi-classical theory for quantum quenches in finite transverse Ising chains
• Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
• Exact Ising model simulation on a quantum computer
• Chaos and statistical relaxation in quantum systems of interacting particles
• First Order Quantum Phase Transition in Adiabatic Quantum Computation
• Quantum relaxation after a quench in systems with boundaries
• Measurement-induced dynamics of many-body systems at quantum criticality
• Finite-size scaling at quantum transitions
• First-order transitions and the performance of quantum algorithms in random optimization problems
• Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
• Coherent and dissipative dynamics at quantum phase transitions
• False vacuum decay in quantum spin chains
• Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
• The quantum adiabatic algorithm and scaling of gaps at first order quantum phase transitions
• Energy spectrum of bound-spinons in the quantum Ising spin-chain ferromagnet
• Finite-size scaling at first-order quantum transitions
• Statistical Mechanics of Systems with Negative Temperature
• Quantum transitions driven by one-bond defects in quantum Ising rings
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Non-Equilibrium Dynamics of a Noisy Quantum Ising Chain: statistics of the work and prethermalization after a sudden quench of the transverse field
• Quantum Ising chains with boundary fields
• Probing ground-state phase transitions through quench dynamics
• Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
• Decay of the metastable phase in d=1 and d=2 Ising models
• Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions
• Dynamic finite-size scaling after a quench at quantum transitions
• Non-adiabatic dynamics across a first order quantum phase transition: Quantized bubble nucleation
• Ground-state fidelity at first-order quantum transitions
• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Dynamic off-equilibrium transition in systems slowly driven across thermal first-order phase transitions
• Dynamical manifestation of Gibbs paradox after a quantum quench
• Finite-size scaling at the first-order quantum transitions of quantum Potts chains
• System size scaling of topological defect creation in a second-order dynamical quantum phase transition
• Competing coherent and dissipative dynamics close to quantum criticality
• On the weak confinement of kinks in the one-dimensional quantum ferromagnet CoNb2O6
• Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions
• Signature of a Continuous Quantum Phase Transition in Nonequilibrium Energy Absorption: Footprints of Criticality on Highly Excited States
• Scaling properties of work fluctuations after quenches at quantum transitions
• Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases
• Finite-size scaling at first-order quantum transitions when boundary conditions favor one of the two phases
• Locating topological phase transitions using nonequilibrium signatures in local bulk observables
• Intrinsic Jump Character of the First-Order Quantum Phase Transitions
• Dynamics after quenches in one-dimensional quantum Ising-like systems
• Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions
• Dissipative dynamics at first-order quantum transitions
• Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Dynamic finite-size scaling at first-order transitions
• Scaling behavior of Ising systems at first-order transitions
• Bridging quantum many-body scar and quantum integrability in Ising chains with transverse and longitudinal fields
• Quantum Quench Dynamics of Geometrically Frustrated Ising Models
• Observation of Near-Critical Kibble-Zurek Scaling in Rydberg Atom Arrays
• Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations
• Statistical properties of eigenvalues for an operating quantum computer with static imperfections
• Tricritical Kibble-Zurek scaling in Rydberg atom ladders
• Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition
• Ising Meson Spectroscopy on a Noisy Digital Quantum Simulator
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Emergent disorder and sub-ballistic dynamics in quantum simulations of the Ising model using Rydberg atom arrays

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