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 (19)
- Thermalization and its mechanism for generic isolated quantum systems
- Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
- Single-Spin Addressing in an Atomic Mott Insulator
- Quantum Quench in the Transverse Field Ising Chain
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Dynamical phase transition in correlated fermionic lattice systems
- Generalized Thermalization in an Integrable Lattice System
- Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
- 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
- Dynamics of thermalisation in small Hubbard-model systems
- Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics
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- 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
- Typicality of Prethermalization
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- 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
- Steady state thermodynamics of two qubits strongly coupled to bosonic environments
- Hydrodynamics and the eigenstate thermalization hypothesis
- 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
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- Localisation in space and time in disordered-lattice open quantum dynamics
- 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
- How two spins can thermalize a third spin
- 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
- 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
- Basis dependence of eigenstate thermalization
- Does a Single Eigenstate of a Hamiltonian Encode the Critical Behaviour of its Finite-Temperature Phase Transition?
- Quantum statistical ensemble for emissive correlated systems
- Theoretical study on thermalization in isolated quantum systems
- Random-matrix approach to time-dependent forcing in many-body quantum systems