Strong-coupling phases of two Hubbard chains with interchain hopping

The T=0 phase diagram for two Hubbard chains with interchain hopping ${\mathit{t}}_{\mathrm{\perp }}$ and on-site repulsion U is derived within a renormalization-group (RG) approach. We explicitly allow for renormalization of the Fermi momenta. A nonzero ${\mathit{t}}_{\mathrm{\perp }}$ drives the chains towards strong coupling, and only for large ${\mathit{t}}_{\mathrm{\perp }}$ is a Luttinger liquid recovered. By use of weak-coupling RG, a qualitative picture of the phase diagram can be obtained. Our calculations show two different strong-coupling regimes: one with nonvanishing effective interchain hopping (〈${\mathit{t}}_{\mathrm{\perp }}$〉≠0), not confining, for small U, and another with 〈${\mathit{t}}_{\mathrm{\perp }}$〉=0, confining, for large U. Numerical diagonalizations for a small cluster support the RG results.