Title: Functional renormalization-group approach to the Pokrovsky-Talapov model via modified massive Thirring fermion model,
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.