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

TL;DR

This paper compares bosonization predictions with exact numerical results for quantum quenches in 1D fermionic systems, revealing that bosonization misses key thermalization features observed in microscopic models.

Contribution

The study demonstrates the limitations of bosonization in capturing the true long-time dynamics of quantum quenches in one-dimensional systems.

Findings

Bosonization predicts persistent critical properties that are not observed.

Numerical results show thermal-like density correlations at small momenta.

Bosonization fails to accurately describe the time evolution after a quantum quench.

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 ${\bar{N}}_q \simeq {\rm const}$ (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.