Temperature and conditions for thermalization after canonical quenches

Abstract

We consider quenches of a quantum system that is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. Technically, our main result is a systematic expansion of the pre- and post-quench canonical ensembles in the quench strength. We first demonstrate how this can be used to predict the system's temperature after the quench from equilibrium properties at the pre-quench temperature. For a thermalizing post-quench system, it furthermore allows us to calculate equilibrium observable expectation values. Finally, in the presence of additional conserved quantities besides the Hamiltonian, we obtain a hierarchy of necessary conditions for thermalization towards the (post-quench) canonical ensemble. At first order, these thermalization conditions have a nice geometric interpretation in operator space with the canonical covariance as a semi-inner product: The quench operator (difference between post- and pre-quench Hamiltonians) and the conserved quantity must be orthogonal in the orthogonal complement of the post-quench Hamiltonian. We illustrate the results numerically for a variety of setups involving integrable and nonintegrable models.

13 pages, 5 figures

References in corpus (24)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Experimental Observation of a Generalized Gibbs Ensemble
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Absence of Thermalization in Nonintegrable Systems
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Many-Body Localization in the Age of Classical Computing
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• From Interacting Particles to Equilibrium Statistical Ensembles
• Correlations in an expanding gas of hard-core bosons
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Thermalization without eigenstate thermalization hypothesis after a quantum quench
• Why are macroscopic experiments reproducible? Imitating the behavior of an ensemble by single pure states
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• Uncovering Local Integrability in Quantum Many-Body Dynamics
• Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
• Thermalization of locally perturbed many-body quantum systems
• Ensemble inequivalence in long-range quantum systems
• Local integrals of motion in dipole-conserving models with Hilbert space fragmentation
• Quantum quench thermodynamics at high temperatures
• Key Observable for Linear Thermalization
• Onsager's regression hypothesis adjusted to quantum systems