Quantum quenches in one-dimensional gapless systems: Does bosonization work?
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. 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
N
¯
q
≃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.