Signatures of a universal jump in the superfluid density in two-dimensional Bose gas with finite number of particles

TL;DR

This study investigates a finite 2D Bose gas and reveals an intermediate phase with unique correlation decay properties, extending understanding of superfluid behavior beyond the BKT transition.

Contribution

It identifies an intermediate phase in finite 2D Bose gases with specific correlation decay characteristics, expanding the phase diagram beyond traditional BKT and thermal phases.

Findings

Existence of an intermediate phase with algebraic correlation decay

Superfluid density approaches Nelson-Kosterlitz prediction with increasing particles

Current-current correlations decay at low momenta in the intermediate region

Abstract

We study, within the classical fields approximation, a two-dimensional weakly interacting uniform Bose gas of a finite number of atoms. By using a grand canonical ensemble formalism we show that such systems exhibit, in addition to the Berezinskii-Kosterlitz-Thouless (BKT) and thermal phases, the intermediate region. This region is characterized by a decay of current-current correlations at low momenta and by an algebraic decay of the first-order correlations with an exponent being larger than the critical value predicted by the BKT theory. The density of the superfluid fraction at the temperature which separates the BKT phase from the intermediate region approaches the one found by Nelson and Kosterlitz for two-dimensional superfluids while the number of atoms is increased.