Uniaxial modulation and the Berezinskii-Kosterlitz-Thouless transition

TL;DR

This paper theoretically investigates how a one-dimensional density modulation affects the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional superfluid, revealing anisotropic effects without dimensional crossover.

Contribution

It introduces a theoretical framework combining analytical and numerical methods to study the impact of density modulation on superfluid phase transitions.

Findings

Increased modulation suppresses the superfluid transition temperature.

The system exhibits anisotropic response with no change in dimensionality.

Physics approaches that of an anisotropic $x$-$y$ model as modulation grows.

Abstract

We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed density modulation along a single axis. The subject is investigated in the context of the $|\psi|^4$ classical field theory, by means of analytical and numerical techniques. We show that, as the amplitude of the modulation increases, the physics of the system approaches that of the anisotropic $x$-$y$ model, with a suppressed superfluid transition temperature and an anisotropic response, but with no dimensional crossover.