The N-chain Hubbard Model in Weak Coupling

Details The N-chain Hubbard Model in Weak Coupling The N-chain Hubbard Model in Weak Coupling

1997-03-06

arxiv.org/abs/cond-mat/9703055v2

Physics

Condensed Matter

Strongly Correlated Electrons

28 pages, 14 figures, add discussions about numerics and experiments

Scientific paper

10.1103/PhysRevB.56.6569

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.

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