Eur. Phys. J. B (2013) 86: 55
https://doi.org/10.1140/epjb/e2012-30978-y

Regular Article

Quantum quenches in one-dimensional gapless systems

¹ Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italy
² Department de Physique Theorique, University of Geneva, 1211 Geneva, Switzerland
³ Democritos Simulation Center CNR-IOM Istituto Officina dei Materiali, Via Bonomea 265, 34136 Trieste, Italy

^a e-mail: becca@sissa.it

Received: 25 October 2012
Published online: 13 February 2013

Abstract

We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. The numerical analysis of the long-time averages shows that density-density correlations at small momenta tend to a non-zero limit, mimicking a thermal behavior. These results are at variance with the bosonization approach, which predicts the presence of long-wavelength critical properties in the long-time evolution. By contrast, the numerical results for finite momenta suggest that the singularities at 2k_F in the density-density correlations and at k_F in the momentum distribution are preserved during the time evolution. The presence of an interaction term that breaks integrability flattens out all singularities, suggesting that the time evolution of one-dimensional lattice models after a quantum quench may differ from that of the Luttinger model.