Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians

Abstract

We present an elementary, general, and semi-quantitative description of relaxation to gaussian and generalized Gibbs states in lattice models of fermions or bosons with quadratic hamiltonians. Our arguments apply to arbitrary initial states that satisfy a mild condition on clustering of correlations. We also show that similar arguments can be used to understand relaxation (or its absence) in systems with time-dependent quadratic hamiltonians, and provide a semi-quantitative description of relaxation in quadratic periodically driven (Floquet) systems.

29 pages, 4 figures. Revised in response to reviewer comments (results unchanged, but expanded introduction and discussion of some points, and added references). Accepted for publication in Physical Review E

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• Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
• Quantum thermalization and Virasoro symmetry
• Generalized thermalization in quantum-chaotic quadratic Hamiltonians
• Correlations and dynamics of tunnel-coupled one-dimensional Bose gases
• Global Quenches after Localised Perturbations
• Normal weak eigenstate thermalization
• Thermalization of locally perturbed many-body quantum systems
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Mechanisms for the emergence of Gaussian correlations
• Relaxation to Gaussian Generalized Gibbs Ensembles in Quadratic Bosonic Systems in the Thermodynamic Limit
• Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models
• Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench
• Connected correlations in partitioning protocols: a case study and beyond
• Single-quasiparticle eigenstate thermalization
• Long-time equilibration can determine transient thermality
• Emergent eigenstate solution for generalized thermalization
• Thermalization in a simple spin-chain model
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Timescales and necessary conditions for hydrodynamization in one-dimensional Bose gases
• On the difference between thermalization in open and isolated quantum systems: a case study
• Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis