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We propose a class of variational wave functions, namely the correlatedvalence bond states, for the frustrated Hamiltonian in the paramagnetic phase.This class of wave functions admits negative amplitude and the same sub-latticepairing when a bipartite lattice is considered, thus suffers from the negativesign problem. However if applied to small systems, the sign problem ismanageable using the standard variational Monte Carlo method. We optimize thewave functions for the J1-J2 Anti ferromagnetic Heisenberg model on a squarelattice in the coupling region J2/J1 \in [0.45 : 0.56] for system sizes L = 4,6, 8. To calculate the correlation functions and the order parameters forlarger systems, we make the extensive Monte Carlo samplings using thevariational parameters optimized at system size L = 8. We find that theparamagnetic phase is a gap-less spin liquid in the entire range of J2/J1 \in[0.45 : 0.56] with a gap-less singlet excitation and a gaped tripletexcitation.

Correlated valence bond state and its study of the spin-1/2 J1-J2 Anti-ferromagnetic Heisenberg model on a square lattice