Successive opening of the Fermi surface in doped N-leg Hubbard ladders

We study the effect of doping away from half-filling in weakly (but finitel y) interacting N-leg Hubbard ladders using renormalization-group and bosoni zation techniques. For small on-site repulsion U, the N-leg Hubbard ladders are equivalent to an N-band model, where at half-filling the Fermi velocit ies are upsilon (1) = upsilon (N) < <upsilon>(2) = upsilon (N-1) < . . . . We then obtain a hierarchy of energy scales, where the band pairs (j, N+1-j ) are successively frozen out. The low-energy Hamiltonian is then the sum o f N/2 [or (N-1)/2 for N odd] two-leg ladder Hamiltonians without gapless ex citations (plus a single chain for N odd with one gapless spin mode)-simila r to the N-leg Heisenberg spin ladders. The energy scales lead to a hierarc hy of gaps. Upon doping away from half-filling, the holes first enter the b and(s) with the smallest gap: For odd N the holes enter first the nonbondin g band (N+1)/2 and the phase is a Luttinger liquid, while for even N, the h oles enter first the band pair (N/2,N/2+1) and the phase is a Luther-Emery liquid, similar to numerical treatments of the t-J model, i.e., at and clos e to half-filling, the phases of the Hubbard ladders for small and large U are the same. For increasing doping, hole pairs subsequently enter at criti cal dopings the other band pairs (j,N+1-j) (accompanied by a diverging comp ressibility): The Fermi surface is successively opened by doping, starting near the wave vector (<pi>/2,pi /2). Explicit calculations are given for th e cases N=3 and 4.