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.
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Coira, E., Becca, F. & Parola, A. Quantum quenches in one-dimensional gapless systems. Eur. Phys. J. B 86, 55 (2013). https://doi.org/10.1140/epjb/e2012-30978-y
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DOI: https://doi.org/10.1140/epjb/e2012-30978-y