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Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models

Emiliano Papa·Alexei M. Tsvelik
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Abstract

In this paper we study the critical exponents of the quantum sine-Gordon and U(1) Thirring models in the incommensurate phase. This phase appears when the chemical potential $h$ exceeds a critical value and is characterized by a finite density of solitons. The low-energy sector of this phase is critical and is described by the Gaussian model (Tomonaga-Luttinger liquid) with the compactification radius dependent on the soliton density and the sine-Gordon model coupling constant $β$. For a fixed value of $β$, we find that the Luttinger parameter $K$ is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value $β^2/8π$ away from it. We describe a possible phase diagram of the model consisting of an array of weakly coupled chains. The possible phases are Fermi liquid, Spin Density Wave, Spin-Peierls and Wigner crystal.

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Emiliano Papa, Alexei M. Tsvelik. 2000-10-30. Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models. https://doi.org/10.1103/physrevb.63.085109

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