Orbital currents and charge density waves in a generalized Hubbard ladder

TL;DR

This paper investigates the presence and behavior of orbital currents and charge density waves in a generalized Hubbard ladder model, revealing long-range order and characteristic oscillations related to doping levels.

Contribution

It combines perturbative RG, bosonization, and DMRG methods to analyze the phase diagram and order parameters in a doped two-leg ladder Hubbard model, highlighting the existence of true long-range order.

Findings

Staggered flux/d-density wave order exhibits long-range correlations.

Charge density and current oscillations have wavelengths inversely proportional to doping.

Order persists beyond weak-coupling predictions, indicating true long-range order.

Abstract

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping delta away from half-filling, finite-size density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = pi(1-delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities.