Gapless Quantum Spin Liquid, Stripe and Antiferromagnetic Phases in Frustrated Hubbard Models in Two Dimensions

Unique features of non-magnetic insulator phase are shown, and phase diagram for $t-t'$ Hubbard model on square lattice is presented. Using the path-integral renormalization group method, we find ntiferromagnetic phase for small next-nearest neighbor transfer $t'$ and stripe (or collinear) phase for large $t'$ in the Mott insulating region of strong on site interaction $U$. For intermediate $t'/t\sim 0.7$ at large $U/t>7$, we find longer-period antiferromagnetic insulator phase with $2\times 4$ structure. In the Mott insulating region, we also find quantum spin liquid (in other words, non-magnetic insulator) phase near the Mott transition to paramagnetic metals. 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 evidences that a nonmagnetic insulating (NMI) phase gets stabilized near the Mott transition with remarkable properties: The 2D Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin zone of the total momentum. It has an interpretation for an unexplored type of a quantum liquid. The present concept is useful in analyzing a variety of experimental results in frustrated magnets including organic BEDT-TTF compounds and $^3$He atoms adsorbed on graphite.