Gapless quantum spin liquid, stripe, and antiferromagnetic phases in frustrated Hubbard models in two dimensions

作者：T. Mizusaki, Masatoshi Imada · 发表于：Physical Review B · 年份：2006 · DOI：10.1103/physrevb.74.014421 · 被引用次数：108 · 研究领域：Advanced Condensed Matter Physics、Physics of Superconductivity and Magnetism、Organic and Molecular Conductors Research

Unique features of the nonmagnetic insulator phase are revealed, and the phase diagram of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model containing the diagonal transfers ${t}^{\ensuremath{'}}$ on a square lattice is presented. Using the path-integral renormalization group method, we find an antiferromagnetic phase for small next-nearest-neighbor transfer ${t}^{\ensuremath{'}}$ and a stripe (or collinear) phase for large ${t}^{\ensuremath{'}}$ in the Mott insulating region of the strong on-site interaction $U$. For intermediate ${t}^{\ensuremath{'}}∕t\ensuremath{\sim}0.7$ at large $U∕t>7$, we find a longer-period antiferromagnetic-insulator phase with $2\ifmmode\times\else\texttimes\fi{}4$ structure. In the Mott insulating region, we also find a quantum spin liquid (in other words, a nonmagnetic insulator) phase near the Mott transition to paramagnetic metals for the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model on the square lattice as well as on the anisotropic triangular lattice. Correlated electrons often crystallize to the Mott insulator usually with some magnetic orders, whereas the ``quantum spin liquid" has been a long-sought issue. We report numerical evidence that a nonmagnetic insulating phase gets stabilized near the Mott transition with remarkable properties: The two-dimensional Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin z...