Amplitude fluctuations in the Berezinskii-Kosterlitz-Thouless phase

Pawel Jakubczyk, Walter Metzner

Published 2016-06-14Version 1

We analyze the interplay of thermal amplitude and phase fluctuations in a $U(1)$ symmetric two-dimensional $\phi^4$-theory. To this end, we derive coupled renormalization group equations for both types of fluctuations. Discarding the amplitude fluctuations, the expected Berezinskii-Kosterlitz-Thouless (BKT) phase characterized by a finite phase stiffness and an algebraic decay of order parameter correlations is recovered at low temperatures. However, in contrast to the widespread expectation, amplitude fluctuations are not innocuous, since their mass vanishes due to a strong renormalization by phase fluctuations. Even at low temperatures the amplitude fluctuations lead to a logarithmic renormalization group flow of the phase stiffness, which ultimately vanishes. Hence, the BKT phase is strictly speaking replaced by a symmetric phase with a finite correlation length, which is however exponentially large at low temperatures. The vortex-driven BKT transition is then rounded to a crossover, which may be practically indistinguishable from a true phase transition in real systems such as $^4$He-films.