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A possibility of the topological Kosterlitz-Thouless~(KT) transition in thePokrovsky-Talapov~(PT) model is investigated by using the functionalrenormalization-group (RG) approach by Wetterich. Our main finding is that thenonzero misfit parameter of the model, which can be related with the lineargradient term (Dzyaloshinsky-Moriya interaction), makes such a transitionimpossible, what contradicts the previous consideration of this problem bynon-perturbative RG methods. To support the conclusion the initial PT model isreformulated in terms of the 2D theory of relativistic fermions using ananalogy between the 2D sine-Gordon and the massive Thirring models. In the newformalism the misfit parameter corresponds to an effective gauge field thatenables to include it in the RG procedure on an equal footing with the otherparameters of the theory. The Wetterich equation is applied to obtain flowequations for the parameters of the new fermionic action. We demonstrate thatthese equations reproduce the KT type of behavior if the misfit parameter iszero. However, any small nonzero value of the quantity rules out a possibilityof the KT transition. To confirm the finding we develop a description of theproblem in terms of the 2D Coulomb gas model. Within the approach the breakdownof the KT scenario gains a transparent meaning, the misfit gives rise to aneffective in-plane electric field that prevents a formation of boundvortex-antivortex pairs.

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