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Physical review. B, Condensed matter

Some critical properties of a planar model via the eigenstates of a fermion system

Trong Tuong Truong, K. D. Schotte

Published Nov 1, 1981• 4 citations
Publisher

Abstract

We show that a soluble Hamiltonian for interacting fermions in one-dimensional conductors generates a classical double Coulomb gas of "electric" and "magnetic" charges and thereby establishes its equivalence with the generalized Villain model in the presence of a fourfold symmetry-breaking term recently studied by L. P. Kadanoff. We use the exact solution of the fermion model to demonstrate how the eight-vertex structure of the mutual fermion scatterings controls its critical behavior.

DOI
10.1103/physrevb.24.5426

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We show that a soluble Hamiltonian for interacting fermions in one-dimensional conductors generates a classical double Coulomb gas of "electric" and "magnetic" charges and thereby establishes its equivalence with the generalized Villain model in the presence of a fourfold symmetry-breaking term recently studied by L. P. Kadanoff. We use the exact solution of the fermion model to demonstrate how the eight-vertex structure of the mutual fermion scatterings controls its critical behavior.
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We show that the one-dimensional Luttinger model generalized to include spin and backward scattering is equivalent to a two-dimensional Coulomb gas. Scaling equations are derived and correlation functions are given simple physical interpretation in terms of the Coulomb gas; e.g., existence of an energy gap can be understood in terms of Debye screening. We conclude that an energy gap exists for ${U}_{\ensuremath{\parallel}}<|{U}_{\ensuremath{\perp}}|$ so that triplet excitations are nondivergent, and we provide physical arguments to support the exponents proposed by Luther and Emery for singlet excitations for general coupling constant.
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