Direct evidence for a gapless Z2 spin liquid by frustrating Neel antiferromagnetism

By direct calculations of the spin gap in the frustrated Heisenberg model on the square lattice, with nearest-(J(1)) and next-nearest-neighbor (J(2)) super-exchange couplings, we provide a solid evidence that the spin-liquid phase in the frustrated regime 0.45 less than or similar to J(2)/J(1) less than or similar to 0.6 is gapless. Our numerical method is based on a variational wave function that is systematically improved by the application of few Lanczos steps and allows us to obtain reliable extrapolations in the thermodynamic limit. The peculiar nature of the nonmagnetic state is unveiled by the existence of S = 1 gapless excitations at k = (pi, 0) and (0, pi). The magnetic transition can be described and interpreted by a variational state that is built from Abrikosov fermions having a Z(2) gauge structure and four Dirac points in the spinon spectrum.