Spectrum statistics in the integrable Lieb-Liniger model

TL;DR

This paper investigates the spectral statistics of the integrable Lieb-Liniger model, revealing conditions under which Poisson statistics emerge and highlighting deviations in long-range correlations.

Contribution

It demonstrates that spectral statistics depend on whether the spectrum or a subset is analyzed, clarifying when Poisson behavior occurs in the Lieb-Liniger model.

Findings

Poisson statistics occur for fixed total momentum at certain interaction strengths and energies

Long-range spectral correlations deviate significantly from Poisson predictions

Spectral properties vary depending on the subset of levels analyzed

Abstract

We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is understanding whether Poisson statistics is a characteristic feature of this model. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. On the other hand, when studying long-range correlations between energy levels, we found strong deviations from the predictions given by a Poisson process.