  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 antiferromagnetic 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~ 0.7 at large U/t>7, we find longer-period antiferromagnetic insulator
phase with 2*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 3He atoms adsorbed on graphite.
