Computing Effective Hamiltonians of Doped and Frustrated Antiferromagnets By Contractor Renormalization

A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high-Tc cuprates. For the S=1/2 Pyrochlore and Kagome antiferromagnets, the effective hamiltonians predict spin-disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.Comment: For the proceedings of the conference on 'Effective Models for Low-Dimensional Strongly Correlated Systems', Peyresq, September 2005. Peyresq Conference. 11 pages, 9 Figure