Correlation functions for a two-dimensional electron system with bosonic interactions and a square Fermi surface

TL;DR

This paper calculates zero-temperature correlation functions for a 2D electron system with a square Fermi surface, revealing unique exponents and dominant charge/spin density wave instabilities.

Contribution

It introduces a bosonic model for 2D electrons with a square Fermi surface, showing differences from Luttinger model exponents and analyzing instabilities.

Findings

Correlation functions are sums of Luttinger-type functions.

Exponents differ from standard Luttinger model.

Charge/spin density wave instabilities dominate for repulsive interactions.

Abstract

We calculate zero-temperature correlation functions for a model of 2D interacting electrons with short-range interactions and a square Fermi surface. The model was arrived at by mapping electronic states near a square Fermi surface with Hubbard-like interactions onto one-dimensional quantum chains, retaining terms which can be written in terms of bosonic density operators. Interactions between orthogonal chains, corresponding to orthogonal faces of the square Fermi surface, are neglected. The correlation functions become sums of Luttinger-type correlation functions due to the bosonic model. However, the correlation function exponents differ in form from those of the Luttinger model. As a consequence, the simple scaling relations found to exist between the Luttinger model exponents, do not carry over to the leading exponents of our model. We find that for repulsive effective interactions, charge-density wave/spin-density wave instabilities are dominant. We do not consider d-wave instabilities here.