Effective lowering of the dimensionality in strongly correlated two dimensional electron gas

TL;DR

This paper investigates a fermion-gauge field system relevant to spin liquids and quantum Hall states, introducing a generalized model with a parameter N, and analyzes its properties in different limits to understand dimensionality effects.

Contribution

It proposes a generalized model with a dimensionless parameter N and analyzes its properties in both large and small N limits, especially focusing on the physically relevant cases of N=1,2.

Findings

Fermion motion becomes one-dimensional at small N

Fermion Green function and response functions derived using bosonization

Model behavior characterized in both N>>1 and N<<1 limits

Abstract

We study a system of fermions interacting with a gauge field which can be used to describe either spin liquid or $\nu=1/2$ Quantum Hall state. We propose a generalized model with a dimensionless parameter $N$. We evaluate the properties of the model in both limits $N \gg 1$ and $N \ll 1$ and deduce the properties of the model in the most physically intersting case of $N=1,2$. At $N \ll 1$ the motion of the fermions becomes one dimensional. This allows us to obtain the fermion Green function and response functions applying bozonization method in this limit.