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

Abstract

We study a system of fermions interacting with a gauge field which can be used to describe either a spin liquid or the \ensuremath{\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\ensuremath{\gg}1 and N\ensuremath{\ll}1 and deduce the properties of the model in the most physically interesting case of N=1,2. At N\ensuremath{\ll}1 the motion of the fermions becomes one dimensional. By applying the bosonization method in this limit, we obtain the fermion Green function and response functions.