Anisotropy crossover in the frustrated Hubbard model on four-chain cylinders

Abstract

Motivated by dimensional crossover in layered organic ${\kappa}$ salts, we determine the phase diagram of a system of four periodically coupled Hubbard chains with frustration at half filling as a function of the interchain hopping ${t_{\perp}/t}$ and interaction strength ${U/t}$ at a fixed ratio of frustration and interchain hopping ${t'/t_{\perp}=-0.5}$. We cover the range from the one-dimensional limit of uncoupled chains (${t_{\perp}/t=0.0}$) to the isotropic model (${t_{\perp}/t=1.0}$). For strong ${U/t}$, we find an antiferromagnetic insulator; in the weak-to-moderate-interaction regime, the phase diagram features quasi-one-dimensional antiferromagnetic behavior, an incommensurate spin-density wave, and a metallic phase as ${t_{\perp}/t}$ is increased. We characterize the phases through their magnetic ordering, dielectric response, and dominant static correlations. Our analysis is based primarily on a variant of the density-matrix renormalization-group algorithm based on an efficient hybrid-real-momentum-space formulation, in which we can treat relatively large lattices albeit of a limited width. This is complemented by a variational cluster approximation study with a cluster geometry corresponding to the cylindrical lattice allowing us to directly compare the two methods for this geometry. As an outlook, we make contact with work studying dimensional crossover in the full two-dimensional system.