Renormalization techniques for quantum spin systems. Ground-state energies

Projection of the Hamiltonian of an antiferromagnetic lattice of spins $\text{1}\text{2}$, without external fields, onto a subspace of the total spinor space gives an approximation for the lowest eigenvalue of this Hamiltonian. Repeated projection results in a series expansion for this approximation. In each projection the form of the Hamiltonian is conserved. The formal structure of this projection technique shows a strong analogy with the Wilson theory or renormalization-group theory of phase transitions. Numerical results are given for linear chains and triangular lattice.Analogous techniques apply to Ising and isotropic XY models in transverse fields.