Scaling exponents in the incommensurate phase of the sine-Gordon and U(1) Thirring models - art. no. 085109

摘要

In this paper we study the critical exponents of the quantum sine-Gordon model 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 beta. For a fixed value of beta, we find that the Luttinger parameter K is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value beta (2)/8 pi 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. [References: 15]