Test of quantum thermalization in the two-dimensional transverse-field Ising model

Abstract

We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.

20 pages, 12 figures. Final published version. Minor changes to v2 including two additional figures and the correction of typos

References in corpus (31)

• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Dephasing and the steady state in quantum many-particle systems
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Generalized Thermalization in an Integrable Lattice System
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Strongly correlated fermions after a quantum quench
• Absence of Thermalization in Nonintegrable Systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Generalized Gibbs Ensembles for Quantum Field Theories
• Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model
• Quantum Quench from a Thermal Initial State
• Quantum relaxation after a quench in systems with boundaries
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions
• Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements

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