Effective lowering of the dimensionality in 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 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.

4 pages