Berezinskii-Kosterlitz-Thouless transition close to zero temperature

TL;DR

This paper investigates the Berezinskii-Kosterlitz-Thouless transition at near-zero temperatures, revealing that quantum fluctuations influence the transition and slightly modify the superfluid density relation.

Contribution

It introduces a quantum critical analysis of the BKT transition using the Keldysh-Schwinger technique and renormalization group methods, extending understanding to low-temperature quantum regimes.

Findings

BKT transition occurs above the crossover temperature at low vortex concentration.

Critical exponent η remains at 1/4 at small temperatures.

Universal relation of superfluid density jump is slightly modified from Nelson and Kosterlitz.

Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the quantum critical point is considered. The approach based on the Keldysh-Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the BKT transition unavoidably occurs at a temperature above the crossover temperature from the thermal fluctuation regime to quantum one. As a result at small temperatures the critical exponent of the BKT transition, $\eta=1/4$, remains unchanged, however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz.