The N-chain Hubbard Model in Weak Coupling

TL;DR

This paper develops a weak-coupling RG method to analyze N-leg Hubbard ladders, revealing broad pairing instabilities with d-wave symmetry and exploring dimensional crossovers as N increases.

Contribution

It introduces a systematic weak-coupling RG technique for N coupled 1D systems, extending previous results and analyzing phase stability and pairing mechanisms.

Findings

Broad regions of phase space are unstable to pairing.

Pairing often exhibits approximate d-wave symmetry.

Dimensional crossovers are discussed as N approaches infinity.

Abstract

We present a systematic weak-coupling renormalization group (RG) technique for studying a collection of $N$ coupled one-dimensional interacting electron systems, focusing on the example of N-leg Hubbard ladders. For $N=2,3$, we recover previous results, and find that also more generally broad regions of the phase space of these models are unstable to pairing, usually with approximate d-wave symmetry. We show how these instabilities can be understood in terms of a fairly conventional ``gap'' function $\Delta$ at the discretized Fermi surface, and describe how this function is calculated. The dimensional crossovers as $N \to \infty$ and as many such ladders are weakly coupled together are also discussed.