Vortex confinement transitions in the modified Goldstone model

Gergely Fejős,Muneto Nitta,Chandrasekhar Chatterjee,Michikazu Kobayashi

doi:10.1103/physrevresearch.2.013081

Gergely Fejős, Muneto Nitta + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.2.013081

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Abstract

This paper suggests a new theoretical model, in which topological objects such as vortices, half-vortices, and solitons coexist. They strongly interact and form topological molecules, triggering a confiment/deconfinement topological phase transition. Its findings provide applications to Josephson-junction arrays of superconducting and nematic liquid crystal films

Highlights

The Berezinskii-Kosterlitz-Thouless (BKT) transition [1,2,3,4] is a topological phase transition of two-dimensional systems, which divides a low-temperature phase with bound vortex-antivortex pairs from a high-temperature phase with free vortices
We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can terminate at one but at two end points in the modified model
The comparison shows that taking into account the derivative of the wave function renormalization factor in the anomalous dimension significantly stabilizes the flow along the line offixed points, as in the improved case the freezing of the flow holds on ∼20 times longer in renormalization group (RG) time t = − log(k/ )

Summary

INTRODUCTION

The Berezinskii-Kosterlitz-Thouless (BKT) transition [1,2,3,4] is a topological phase transition of two-dimensional systems, which divides a low-temperature phase with bound vortex-antivortex pairs from a high-temperature phase with free vortices. It turned out that the conventional Wetterich formulation of the method was capable of showing signs in the two-dimensional linear O(2) or Goldstone model of the line of fixed points that is responsible for the topological nature of the phase transition This is remarkable in the sense that no vortices need to be introduced explicitly, as opposed to the older real-space RG description [4]. It is worth pointing out that recently in a dual lattice formulation of the FRG, Krieg and Kopietz [45] exactly reproduced the RG flow equations derived by Kosterlitz and Thouless [4] and the existence of a true line of fixed points was established in terms of a momentum space RG It would be interesting, to develop a scheme in the ordinary Wetterich formulation of the FRG, which could lead to a similar result. In Appendix A we show how to derive the Hamiltonian of the modified Goldstone model from the microscopic lattice model of the modified XY model, while in Appendix B we derive some of the corresponding flow equations of the FRG

Modified Goldstone model

Classical solutions

Flow equation: A review

Local potential approximation

Wave function renormalization improvement

Phase structure

NUMERICAL SIMULATIONS

Correlation function and transition temperature

Preparation

Superfluid density and specific heat

Vortex configurations

SUMMARY