Bipairing and the Stripe Phase in 4-Leg Ladders

Density Matrix Renormalization Group (DMRG) calculations on 4-leg t-J and Hubbard ladders have found a phase exhibiting "stripes" at intermediate doping. Such behavior can be viewed as generalized Friedel oscillations, with wavelength equal to the inverse hole density, induced by the open boundary conditions. So far, this phase has not been understood using the conventional weak coupling bosonization approach. Based on studies from a general bosonization proof, finite size spectrum, an improved analysis of weak coupling renormalization group equations and the decoupled 2-leg ladders limit, we here find new types of phases of 4-leg ladders which exhibit "stripes". They also inevitably exhibit "bipairing", meaning that there is a gap to add 1 or 2 electrons (but not 4) and that both single electron and electron pair correlation functions decay exponentially while correlation functions of charge 4 operators exhibit power-law decay. Whether or not bipairing occurs in the stripe phase found in DMRG is an important open question.