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We study the dimensional crossover from 1D to 2D in half-filled and lightlydoped, weakly interacting N-leg Hubbard ladders. In this case, the Hubbardladders are equivalent to a N-band model. Using renormalization grouptechniques, we find, that the half-filled ladders exhibit (in the spin-sector)an odd-even effect only below a crossover energy E_{c}\propto exp[-a exp(c N)](a<<1 and c\sim 1), i.e., below E_{c}, the interactions take place only withinband pairs (j,N+1-j) [and within the band (N+1)/2 for N odd], such thateven-leg ladders are an insulating spin-liquid, while odd-leg ladders have onegapless spinon-mode. In contrast, above the energy-scale E_{c}, all bands areinteracting with each other and the system is a 2D-like (insulating)antiferromagnet; we obtain an analytical expression for the Hamiltonian whichis similar to the 2D Heisenberg antiferromagnet. Bosonization techniques show,that the Mott insulator is as well below and above E_{c} of the same type as inN/2 half-filled two-leg ladders; the charge-sector is therefore the same in 1Dand 2D. Doping away from half-filling, we find that the effect of an increasingdoping is very similar to decreasing the number of legs N: In both casesinteractions between unpaired bands are suppressed and the antiferromagneticcorrelations are reduced. The resulting band pairs (j,N+1-j) are theninsulating spin-liquids and when doped, there is a spin-gap, but phasecoherence exists only within pairs of Fermi momenta (k_{Fj},pi-k_{Fj}) and(pi-k_{Fj},k_{Fj}). At higher doping levels delta_{c}=delta_{c}(N), phasecoherence between all bands sets in and the system becomes a 2D-like d-wavesuperconductor (delta_{c} goes to 0 in the 2D limit).Comment: 12 pages, 5 figures, to be published in Phys. Rev.

Dimensional crossover in half-filled and lightly dopedN-leg Hubbard ladders