Dynamical properties of two doped, coupled Hubbard chains

Abstract

Using quantum Monte Carlo (QMC) simulations combined with Maximum Entropy analytic continuation as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at small doping. The behavior of the single-particle spectral weight $A({\bf k},ω)$ as a function of hopping anisotropy $t_\perp/t$ at intermediate interaction strength is dominated by the transition from one-band behavior at large $t_\perp/t$ to two-band behavior at small $t_\perp/t$, although interaction effects such as band-narrowing, a shift of spectral weight to higher energies in the unoccupied antibonding band and reflected structures due to short-range antiferromagnetic correlations are also present. A single-particle gap is resolved in the intermediate $t_\perp/t$ Luther-Emery phase using Density Matrix Renormalization Group calculations. The dynamical spin and charge susceptibilities show features of the expected bonding-band Luttinger liquid behavior, as well as higher-energy features due to local excitations between the chains at large $t_\perp/t$, and evolve towards the behavior of two uncoupled chains as $t_\perp/t$ is reduced. For the one hole, large $t_\perp/t$ case, we make a detailed comparison between the QMC data and an approximation based on local rung states. At isotropic coupling and somewhat larger doping, we find that the dispersion of the single-particle bands is essentially unrenormalized from that of the noninteracting system, and that the spin and charge response functions have features also seen in random-phase-approximation calculations.