Dynamical properties of two doped, coupled Hubbard chains

TL;DR

This study uses advanced numerical and analytical methods to explore the dynamical properties of doped two-chain Hubbard models, revealing a transition from one-band to two-band behavior and characterizing spin and charge excitations across different coupling regimes.

Contribution

It provides a comprehensive analysis of the dynamical spectral functions and susceptibilities in doped coupled Hubbard chains, highlighting the evolution of behavior with interchain coupling and doping, and comparing numerical results with analytical approximations.

Findings

Transition from one-band to two-band spectral behavior with changing interchain hopping

Observation of a single-particle gap in the Luther-Emery phase at intermediate coupling

Features of Luttinger liquid behavior in spin and charge susceptibilities

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 $A({\bf k},\omega)$ 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.