Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model

TL;DR

This paper investigates the one-dimensional Bose-Hubbard model to identify signatures of the Berezinskii-Kosterlitz-Thouless transition through on-site atom number fluctuations and their derivatives, providing insights into quantum phase transitions in cold atom systems.

Contribution

It demonstrates that derivatives of on-site atom number variance exhibit extrema off the critical point, offering potential evidence of the BKT transition in the Bose-Hubbard model.

Findings

Derivatives of atom number variance have extrema away from the critical point.

Nearest-neighbor correlations are characterized in the study.

Results are obtained for systems with one or two atoms per site.

Abstract

We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.