Weak-coupling phase diagram of the two-chain Hubbard model

We present a general method for determining the phase diagram of systems of a finite number of one-dimensional Hubbard-like systems coupled by single-particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two-chain Hubbard model, providing controlled results for arbitrary doping and interchain hopping. Of nine possible states which could occur in such a spin-1/2 ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one-dimensional analog of a superconductor.