Boson, Symplectic and Other Replicas for Simple Hamiltonians

Abstract

We present a linearization method for some simple (naturally tridiagonal) Hamiltonians. For the ground states it is equivalent to the lowest approximation in the coupled cluster formalism and its extension to excited states is straightforward. Then we construct sets of equivalent Hamiltonians (boson or symplectic replicas) that produce the same secular problem. In general they are not manifestly Hermitian. We show how to deal with this problem and we extract mean fields that describe both the normal and symmetry breaking regimes and at the same time incorporate variationally terms usually thought of as correlations.