Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model

We numerically study Heisenberg models on modified triangular lattices, and show that a weak next-nearest-neighbor exchange interaction added to a simple triangular lattice, namely, the equilateral triangular lattice with only the nearest-neighbor exchange is sufficient to stabilize a quantum spin liquid against the antiferromagnetic order widely accepted as the ground state of the simple triangular model. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic and spin-liquid phases as well as inside the spin-liquid phase, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents z+eta sim 1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.