Variational bound for the energy of two- dimensional quantum antiferromagnet

We obtain the variational upper bound for the groundstate energy of twodimensional antiferromagnetic Heisenberg model on a square lattice at arbitrary value of the anisotropy parameter using the two-dimensional generalization of Jordan-Wigner transformation. Our result can be considered as an upper bound for the perturbation theory series about the Ising limit. At present time two dimensional quantum spin systems attract much attention in connection with the problem of high-Tc superconductivity. For the antiferromagnetic Heisenberg model at some values of the anisotropy parameter the existence of the longrange order was proved [1], however the exact ground state is not known. Apart from the linear spin wave theory [2] various methods to evaluate the ground state energy for the Heisenberg antiferromagnet were proposed. For instance the perturbation theory and the cluster expansion about the Ising limit were used [3]. However, although the convergence of the series of the perturbation theory is good these estimates are not the variational ones. At the same time the energy corresponding to any reasonable variational ground-state wave function cannot be computed exactly (for example of these calculations see ref.[4]). Finally at present time the accuracy of the numerical