DMRG and weak coupling studies of the two-leg Hubbard ladder

The Hubbard model is of paradigmatic significance in the study of highly correlated electron systems. Hubbard ladders are particularly interesting as they exhibit a subtle interplay between multiple phases even at weak coupling. Here, we reexamine the ground state phase diagram of the two-leg ladder in the limit of asymptotically weak coupling, an approach pioneered by Balents and Fisher (BF). Among other things we find that the presence of a dangerously irrelevant operator leads to an instability of a previously predicted partially gapped phase. The result is a Luther-Emery (LE) liquid - the 1D analogue of a superconductor - characterized by a hierarchy of energy scales: the principle gap depends exponentially on 1/U in the asymptotic U → 0⁺ limit, as found by BA, while the additional gaps are smaller still by factors of U^1/2 compared to the dominant gap. Using DMRG to study the same ladder for intermediate values of U (as small as U = 4t), we find qualitative behavior (LE phase and the existence of two distinct gap scales) similar to that predicted by the weak coupling theory.