1205.2967 (Emanuele Coira et al.)

Quantum quenches in one-dimensional gapless systems: Does bosonization
work?    [PDF]

Emanuele Coira, Federico Becca, Alberto Parola

We present a comparison between the bosonization results for quantum quenches [M. A. Cazalilla, \prl {\bf 97}, 156403 (2006)] and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. We show that important features are missed by the bosonization technique, which predicts the persistence of long-wavelength critical properties in the long-time evolution. Instead, numerical analysis provides puzzling evidences: while the momentum distribution appears to be consistent with the presence of a singularity at $k_F$, density-density correlations at small momenta clearly display a thermal-like behavior, namely ${\bar{N}}_q \simeq {\rm const}$ (where the overbar indicates the long-time average). This feature at small momenta is preserved in presence of an interaction term that breaks integrability, together with a rounding of the singularities at finite $q$'s, showing that the bosonization approach is not able to represent the time evolution of generic one-dimensional models after a quantum quench.

View original: http://arxiv.org/abs/1205.2967