A new class of exactly solvable interacting fermion models in one dimension

TL;DR

This paper introduces a novel exactly solvable 1D interacting fermion model with nontrivial correlation exponents, providing insights into Luttinger's original solution and extending to lattice and symmetry generalizations.

Contribution

It presents a new class of exactly solvable 1D fermion models with interaction-dependent exponents and discusses their relation to Luttinger's theory and possible generalizations.

Findings

Model solvable via unitary transformation

Correlation functions show nontrivial exponents

Extensions to lattice and symmetry cases

Abstract

We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary transformation. Nevertheless, correlation functions exhibit nontrivial interaction-dependent exponents. A similar model defined on a lattice is introduced and solved. Various generalizations, e.g. to the case of internal symmetries of the fermions, are discussed. The present treatment also clarifies certain aspects of Luttinger's original solution of the ``Luttinger model''.