Thermalisation of Local Observables in Small Hubbard Lattices
arXiv:1204.3036 · doi:10.1103/PhysRevA.86.023609
Abstract
We present a study of thermalisation of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalises with the rest of the system as its environment. We explore numerically the existence of thermalisation over a range of system parameters, such as the interaction strength, system size and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalisation over a wide range of parameters and that interactions are crucial for efficient thermalisation of small systems. We relate this thermalisation behaviour to the eigenstate thermalisation hypothesis and quantify numerically the extent to which eigenstate thermalisation holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalisation.
22 pages, 23 figures
References in corpus (39)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- 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
- A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
- Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
- Single-Spin Addressing in an Atomic Mott Insulator
- Canonical Typicality
- Quantum Quench in the Transverse Field Ising Chain
- Quantum mechanical evolution towards thermal equilibrium
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Dynamical phase transition in correlated fermionic lattice systems
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Generalized Thermalization in an Integrable Lattice System
- Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
- Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
- Absence of Thermalization in Nonintegrable Systems
- Typicality for Generalized Microcanonical Ensembles
- Nonthermal steady states after an interaction quench in the Falicov-Kimball model
- Quantum Quenches, Thermalization and Many-Body Localization
- Quantum chaos and thermalization in gapped systems
- Quantum Quench from a Thermal Initial State
- Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates
- Thermalization of a strongly interacting closed spin system: From coherent many-body dynamics to a Fokker-Planck equation
- Thermalization in a coherently driven ensemble of two-level systems
- Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates
- Wavepacket dynamics in energy space, RMT and quantum-classical correspondence
- Einselection without pointer states
- Origin of the Canonical Ensemble: Thermalization with Decoherence
- Approach to equilbrium in nano-scale systems at finite temperatur
- Non-thermal statistics in isolated quantum spin clusters after a series of perturbations
- Emergence of canonical ensembles from pure quantum states
- Dynamics of thermalisation in small Hubbard-model systems
- A necessary condition for the thermalization of a quantum system coupled to a quantum bath
- Failure of random matrix theory to correctly describe quantum dynamics
- Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics
- Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization
Cited by in corpus (40)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Eigenstate Thermalization Hypothesis
- Finite-size scaling of eigenstate thermalization
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- Signatures of many-body localisation in a system without disorder and the relation to a glass transition
- The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
- Relaxation theory for perturbed many-body quantum systems versus numerics and experiment
- Typicality of Prethermalization
- Dynamics of thermalization and decoherence of a nanoscale system
- Temporal decay of Neel order in the one-dimensional Fermi-Hubbard model
- Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current
- Hydrodynamics and the eigenstate thermalization hypothesis
- Steady state thermodynamics of two qubits strongly coupled to bosonic environments
- Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State
- Fluctuation Theorems and the Generalised Gibbs Ensemble in Integrable Systems
- Equilibration of quantum hard rods in one dimension
- Eigenstate Thermalization and Spontaneous Symmetry Breaking in the One-Dimensional Transverse-Field Ising Model with Power-Law Interactions
- Entropy and Temperature in finite isolated quantum systems
- Assigning Temperatures to Eigenstates
- Localisation in space and time in disordered-lattice open quantum dynamics
- Typical, finite baths as a means of exact simulation of open quantum systems
- Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
- Non-linear response to electric field in extended Hubbard models
- Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model
- Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
- Universal short-time response and formation of correlations after quantum quenches
- Canonical density matrices from eigenstates of mixed systems
- Typical equilibrium state of an embedded quantum system
- Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer
- Predicting Imperfect Echo Dynamics in Many-Body Quantum Systems
- How two spins can thermalize a third spin
- Estimate of equilibration times of quantum correlation functions in the thermodynamic limit based on Lanczos coefficients
- Quantum Joule Expansion of One-Dimensional Systems
- Persistent many-body quantum echoes
- Quantum statistical ensemble for emissive correlated systems
- Random-matrix approach to time-dependent forcing in many-body quantum systems
- Basis dependence of eigenstate thermalization
- Does a Single Eigenstate of a Hamiltonian Encode the Critical Behaviour of its Finite-Temperature Phase Transition?
- Theoretical study on thermalization in isolated quantum systems