Thermalization in the Two-Body Random Ensemble

Abstract

Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and specially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, like the energy and structure of the initial state, or the dimension of the Hilbert space. We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originated at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable. As the strength of the residual interaction is increased an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems. When all the signatures of chaos are fulfilled, including the quasi complete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators. Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.

22 pages, 9 figures, new version with some modifications in presentation, accepted for publication in Journal of Statistical Mechanics

References in corpus (10)

• Thermalization and its mechanism for generic isolated quantum systems
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• 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
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
• Periodic-Orbit Theory of Level Correlations

Cited by in corpus (17)

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• Off-diagonal matrix elements of local operators in many-body quantum systems
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
• Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
• Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Temperature of a single chaotic eigenstate
• Reappraisal of the limit on the variation in $\alpha$ implied by Oklo
• Localization-Delocalization Transitions in Bosonic Random Matrix Ensembles
• Random Matrix Ensembles For Many-Body Quantum Systems
• Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions
• Modelling equilibration of local many-body quantum systems by random graph ensembles
• Localized Thermal States
• Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
• Non-Equilibrium Many-Body Dynamics Following A Quantum Quench
• Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions