Finite-size effects in global quantum quenches: Examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model

Journal Article · Sat May 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.053604· OSTI ID:21408862

Roux, Guillaume ^[1]

---

1. Laboratoire de Physique Theorique et Modeles Statistiques, Centre National de la Recherche Scientifique, and Universite Paris-Sud, UMR8626, Batiment 100, FR-91405 Orsay (France)

We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the time-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the ''thermalized'' regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.

• OSTI ID: 21408862
• Journal Information: Physical Review. A, Vol. 81, Issue 5; Other Information: DOI: 10.1103/PhysRevA.81.053604; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSONS
COMPARATIVE EVALUATIONS
DENSITY MATRIX
ENERGY SPECTRA
EQUILIBRIUM
EXCITATION
GROUND STATES
HUBBARD MODEL
INTERACTIONS
ONE-DIMENSIONAL CALCULATIONS
TRAPS
CRYSTAL MODELS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EVALUATION
MATHEMATICAL MODELS
MATRICES
SPECTRA