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Scaling exponents in the incommensurate phase of the sine-Gordon and U(1) Thirring models

2001; American Physical Society; Volume: 63; Issue: 8 Linguagem: Inglês

10.1103/physrevb.63.085109

1095-3795

Emiliano Papa, A. M. Tsvelik,

Algebraic structures and combinatorial models

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 $\ensuremath{\beta}.$ For a fixed value of $\ensuremath{\beta},$ we find that the Luttinger parameter K is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value ${\ensuremath{\beta}}^{2}/8\ensuremath{\pi}$ 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.