Orbital currents and charge density waves in a generalized Hubbard ladder (Q2368897)

This paper is devoted to a generalized Hubbard model on the two-leg ladder at zero temperature in the parameter region with staggered flux (SF)/\(d\)-density wave (DDW) order, focusing on the case of finite hole doping away from half filling. The approximate location of this parameter region with long-range SF/DDW order in the weakly interacting half-filled ladder is found from a calculation of the phase diagram of corresponding model, which is done by using abelian bosonization and semiclassical considerations to analyze the low-energy effective theory, resulting from a one-loop renormalization-group (RG) flow. Then, the finite system density-matrix renormalization-group (DMRG) calculations are used to study the SF/DDW phase in doped ladders, for intermediate-strength interactions and ladder sizes up to 200 rungs. For the hole dopings considered, currents are found to be large and show no evidence of decay. As the doping is increased the currents in the SF/DDW phase decrease in magnitude and for sufficiently strong doping SF/DDW order becomes completely suppressed. The rung currents found in the doped SF/DDW phase vary both in sign and magnitude, corresponding to an ordering wavevector \(2kF = p(1 - d)\), where \(d\) is the hole doping away from half filling. It is found, that a charge density moduilation coexists with the orbital currents in the doped SF/DDW phase. The staggered rung current and the rung electron density both show a periodic spatial variation with characteristic wave-lengths \(2/d\) and \(1/d\), respectively, corresponding to ordering wavevectors \(2kF\) and \(4kF\) for the currents and density modulation. While, the most of the DMRG results can be qualitatively understood from weak coupling RG/bosonization arguments, it is shown the DMRG results are consistent with a true long-range order scenario for the currents and densities.