Decimation approach in quantum systems

The possibility of applying the decimation method to quantum systems is critically examined in two systems: the anisotropic Heisenberg hamiltonian and spinless interacting fermions. We show that, in general, the decimation transformation does not conserve the ground state of the system and therefore badly describes the T=O fixed point. This in turn, within the Migdal-Kadanoff approach, introduces several spurious effects, whose origin and consequences are analyzed in detail for different dimensions. (orig.)