Dynamical Properties of Two Coupled Hubbard Chains at Half-filling

TL;DR

This study investigates the dynamical properties of two coupled Hubbard chains at half-filling using QMC simulations and analytical models, revealing a transition from four-band to two-band insulator and characterizing spin and charge excitations.

Contribution

It provides a comprehensive analysis of one- and two-particle spectra in coupled Hubbard chains, combining numerical and analytical methods to elucidate the effects of interchain hopping.

Findings

Transition from four-band to two-band insulator with increasing interchain hopping

Analytical model accurately describes spectral features at large hopping

Coherent bands and incoherent backgrounds characterized in spectra

Abstract

Using grand canonical 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 half-filling. The one-particle spectral weight function, $A({\bf k},\omega)$, undergoes a qualitative change with interchain hopping $t_\perp$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large $t_\perp$. For smaller $t_\perp$, $A({\bf k}, \omega)$ is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange $J$ reasonably well-described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral $t$, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large $t_\perp$ and to the results of spin-wave theory for small $t_\perp$.