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arXiv:1403.4497 · Physical Review B

One-dimensional spin liquid, collinear, and spiral phases from uncoupled chains to the triangular lattice

Luca F. Tocchio, Claudius Gros, Roser Valentí, Federico Becca

Published Jun 6, 2014• 31 citations
arXivHTMLPDF

Abstract

We investigate the Hubbard model on the anisotropic triangular lattice with two hopping parameters $t$ and ${t}^{\ensuremath{'}}$ in different spatial directions, interpolating between decoupled chains ($t=0$) and the isotropic triangular lattice ($t={t}^{\ensuremath{'}}$). Variational wave functions that include both Jastrow and backflow terms are used to compare spin-liquid and magnetic phases with different pitch vectors describing both collinear and coplanar (spiral) order. For relatively large values of the on-site interaction $U/{t}^{\ensuremath{'}}\ensuremath{\gtrsim}10$ and substantial frustration, i.e., $0.3\ensuremath{\lesssim}t/{t}^{\ensuremath{'}}\ensuremath{\lesssim}0.8$, the spin-liquid state is clearly favored over magnetic states. Spiral magnetic order is only stable in the vicinity of the isotropic point, while collinear order is obtained in a wide range of interchain hoppings from small to intermediate frustration.

DOI
10.1103/physrevb.89.235107

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Motivated by dimensional crossover in layered organic $\ensuremath{\kappa}$ 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 ${t}_{\ensuremath{\perp}}/t$ and interaction strength U/tU/tU/t at a fixed ratio of frustration and interchain hopping ${t}^{\ensuremath{'}}/{t}_{\ensuremath{\perp}}=\ensuremath{-}0.5$. We cover the range from the one-dimensional limit of uncoupled chains (${t}_{\ensuremath{\perp}}/t=0.0$) to the isotropic model (${t}_{\ensuremath{\perp}}/t=1.0$). For strong U/tU/tU/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 ${t}_{\ensuremath{\perp}}/t$ 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.