# Functional renormalization-group approach to the Pokrovsky-Talapov model via modified massive Thirring fermion model

## TL;DR

This paper uses a functional renormalization-group approach to show that a nonzero misfit parameter in the Pokrovsky-Talapov model prevents the topological Kosterlitz-Thouless transition, contradicting previous non-perturbative RG results.

## Contribution

The study reformulates the PT model via a relativistic fermion theory and demonstrates that the misfit parameter inhibits the KT transition, providing a new perspective on the model's phase behavior.

## Key findings

- Nonzero misfit parameter rules out KT transition.
- Reformulation in fermionic terms introduces an effective gauge field.
- Breakdown of KT transition explained by an in-plane electric field.

## Abstract

A possibility of the topological Kosterlitz-Thouless~(KT) transition in the Pokrovsky-Talapov~(PT) model is investigated by using the functional renormalization-group (RG) approach by Wetterich. Our main finding is that the nonzero misfit parameter of the model, which can be related with the linear gradient term (Dzyaloshinsky-Moriya interaction), makes such a transition impossible, what contradicts the previous consideration of this problem by non-perturbative RG methods. To support the conclusion the initial PT model is reformulated in terms of the 2D theory of relativistic fermions using an analogy between the 2D sine-Gordon and the massive Thirring models. In the new formalism the misfit parameter corresponds to an effective gauge field that enables to include it in the RG procedure on an equal footing with the other parameters of the theory. The Wetterich equation is applied to obtain flow equations for the parameters of the new fermionic action. We demonstrate that these equations reproduce the KT type of behavior if the misfit parameter is zero. However, any small nonzero value of the quantity rules out a possibility of the KT transition. To confirm the finding we develop a description of the problem in terms of the 2D Coulomb gas model. Within the approach the breakdown of the KT scenario gains a transparent meaning, the misfit gives rise to an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.