Generalized Jastrow variational method for dense Fermi systems

Vijay R. Pandharipande

H. B. Ghassib

Kevin E. Schmidt

"A theory is developed to allow the systematic calculation of the properties of quantum fluids given the microscopic two-body potential. Physical arguments are used to construct a correlation operator that approximately transforms the states of a non-interacting system into the corresponding states of the interacting-system. The theory can be regarded as a microscopic realization of Landau's assumption of a one-to-one correspondence between the non-interacting and interacting states. It is variational since the correlation operator is determined by minimizing E(p) the expectation value of the ground-state energy. We first give a survey of various other many-body theories including the simpler Jastrow variational method. Differential equations are derived to calculate the correlation operator and the related Jastrow correlation"" function. A comparison of results in several Bose systems with various methods is given. The Fermi hypernetted chain integral equations are generalized to allow the calculation of E(p) in Fermi systems, using the correlation operator wave function. The method is applied to liquid 3He and the v2-model of nuclear matter. In 3He the correlation operator gives results in much closer agreement with experiment than that with the Jastrow wave function. A new set of hypernetted chain equations are then derived to allow the calculation of the excited st;ate energies in Bose systems. The theory is then applied to the calculation of the single quasi-particle excitation spectrum of liquid 4He. The spectrum is found to be a stringent test on the form of the correlation operator, deficiencies in the correlation operator giving corresponding errors in the spectrum. Good results are obtained for the density dependence of the roton energy. A variational principle for the free energy is used to generalize the correlation operator technique to finite temperatures. Results are given for the finite temperature properties of the v8-model of nuclear matter."

T.S. Walhout, R. Cenni, Adelchi Fabrocini +1 more

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.

O.O. Tursunov, O. V. Zhirov

Yang Xian

We study many-body correlations in the ground state of a general quantum system of bosons or fermions by including an additional Jastrow function in our recently proposed variational coupled-cluster method. Our approach combines the advantages of state-dependent correlations in the coupled-cluster theory and of the strong, short-ranged correlations of the Jastrow function. We apply a generalized linked-cluster expansion for the Jastrow wave function and provide a detailed analysis for practical evaluation of the Hamiltonian expectation value as an energy functional of the Jastrow function and the bare density-distribution functions introduced and calculated in our earlier publications; a simple, first-order energy functional is derived and detailed formulas for the higher-order contributions are provided. Our energy functional does not suffer the divergence as most coupled-cluster calculations often do when applying to Hamiltonians with hardcore potentials. We also discuss possible applications of our technique, including applications to strongly correlated fermion systems.