Theoretical study on thermalization in isolated quantum systems
arXiv:1901.01481
Abstract
Understanding how isolated quantum systems thermalize has recently gathered renewed interest almost 100 years after the first work by von Neumann, thanks to the experimental realizations of such systems. Experimental and numerical pieces of evidence imply that nonintegrability of the system plays an important role in thermalization. Nonintegrable systems that conserve energy alone are expected to be effectively described by the (micro)canonical ensemble due to the so-called eigenstate thermalization hypothesis (ETH) in the thermodynamic limit. In contrast, it is expected that stationary states in integrable systems are described not by the canonical ensemble but by the generalized Gibbs ensemble (GGE) due to the existence of many nontrivial conserved quantities. In this thesis, we study thermalization and its mechanism in nonintegrable systems from two perspectives. We first study how well the ETH and its finite-size corrections can be predicted by random matrix theory (RMT). Next, we present our study on the emergence of the GGE in a nonintegrable system with an extensive number of local symmetries.
Master theses (the original version submitted to the University of Tokyo in January 2017), 171 pages
References in corpus (36)
- Many-Body Physics with Ultracold Gases
- Classification of topological insulators and superconductors in three spatial dimensions
- Thermalization and its mechanism for generic isolated quantum systems
- Localization of interacting fermions at high temperature
- Many body localization in Heisenberg XXZ magnet in a random field
- Phenomenology of fully many-body-localized systems
- Quantum Quench in the Transverse Field Ising Chain
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Experimental Observation of a Generalized Gibbs Ensemble
- Many-body localization in periodically driven systems
- 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
- Dynamical phase transition in correlated fermionic lattice systems
- Many-Body Localization in a Quasiperiodic System
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Anomalous diffusion and Griffiths effects near the many-body localization transition
- Strong and weak thermalization of infinite non-integrable quantum systems
- 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
- Signatures of Many-Body Localization in a Controlled Open Quantum System
- Absence of Thermalization in Nonintegrable Systems
- Typicality for Generalized Microcanonical Ensembles
- Anomalous thermalization in ergodic systems
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Eigenstate thermalization within isolated spin-chain systems
- Validity of the GGE for quantum quenches from interacting to noninteracting models
- Generalized Gibbs Ensembles for Quantum Field Theories
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Generalized TBA and generalized Gibbs
- From Interacting Particles to Equilibrium Statistical Ensembles
- Generalization of von Neumann's Approach to Thermalization
- Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
- Weak eigenstate thermalization with large deviation bound