Path integral variational methods for strongly correlated systems

Abstract

We introduce an alternative approach to highly correlated systems that generalizes the Fermi hypernetted chain and correlated basis function techniques. While the latter approaches can be applied only to systems for which a nonrelativistic wave function can be defined, the present approach is based on the variation of a trial Hamiltonian within a path-integral framework and thus can be applied also to relativistic and field theoretical problems. We derive a diagrammatic scheme for the present approach and show how a particular choice of trial Hamiltonian corresponds exactly to the use of a Jastrow correlated ansatz for the wave function in the Fermi hypernetted chain approach. We show how our approach can be used to find upper bounds to ground-state energies in systems that the Fermi hypernetted chain approach cannot handle, including those described by an energy-dependent effective Hamiltonian. We demonstrate our approach by applying it to a quantum field theoretical system of interacting pions and nucleons. \textcopyright{} 1996 The American Physical Society.