Exact solution of a 2D interacting fermion model

TL;DR

This paper presents an exact solution to a 2D interacting fermion model, demonstrating Luttinger-liquid behavior with algebraic decay of correlations, using bosonization and renormalization techniques.

Contribution

It provides an exact analytical solution to a 2D interacting fermion model, linking it to lattice fermions and analyzing correlation functions with renormalization.

Findings

Correlation functions decay algebraically with non-trivial exponents

Model exhibits Luttinger-liquid behavior in 2D

Renormalization removes cutoffs, revealing physical properties

Abstract

We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.