Scaling function for energy-density correlations: Dispersion theory and?-expansion forT>T c

A. Knoll

Hong-Kang Zhao, Mu-Lin Yan

The leading behavior of the energy density Green function in Ising quantum field theory is investigated. By using the scaling theory and cluster expansion, we obtain the function of Ising field model in the presence of an external magnetic field as T → T c - from Bariev's correlation function.

V. I. Kuz’min, Sergey V. Nikolaev, Sergei G. Ovchinnikov

Electronic dispersion and density of states (DOS) have been calculated for the Hubbard model and the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}^{*}$ models with three-site correlated hopping by the cluster perturbation theory. We have found a rather strong quantitative difference both in dispersion and DOS at all doping for the Hubbard and $t\ensuremath{-}J$ models at the energy scale $\ensuremath{\omega}\ensuremath{\gtrsim}t$. The three-site correlated hopping addition results in an almost negligible difference for the Hubbard and $t\ensuremath{-}{J}^{*}$ models. Close to the Fermi energy, at the scale $\ensuremath{\omega}\ensuremath{\lesssim}J$, the electronic structure of all three models is similar. We have found the line of zeros of the Green function for the $t\ensuremath{-}J$ model that has been previously obtained for the Hubbard model by cellular dynamical mean-field theory calculations.

Alexander Migdal

J. W. Clark, MANFRED L. RISTIG

A nonperturbative derivation of the Brueckner approximation to the ground-state energy of nuclear matter (with standard choice of hole and particle energies) is given within the framework of the method of correlated basis functions. The structure of the factor-cluster (FIY) expansion of the expectation value of the Hamiltonian with respect to a trial function incorporating short-range correlations in a general fashion, is analyzed for a uniform extended medium of fermions. With a special choice of correlated wave function, the Brueckner approximation is extracted from the FIY expansion by selective summation of two-body combination terms to all orders in the smallness parameter $\ensuremath{\kappa}$ associated, in this case, with both Brueckner-Bethe-Goldstone and FIY energy expansions. A reexamination of the numerical comparison of conventional Brueckner and Jastrow methods carried out earlier for two simple models of nuclear matter leads to the conclusion that it is inadvisable, at least in a Jastrow calculation satisfying the average Pauli condition, to incorporate the $O(\ensuremath{\kappa})$ contribution of the analog of the dispersion correction of reaction-matrix theory without at the same time including the $O(\ensuremath{\kappa})$ contribution of the analog of the Bethe-Faddeev term. For the uniform extended medium for the Jastrow choice of wave function, there is a formal cancellation of these two three-body contributions, the scale of this cancellation being governed by the size of $\ensuremath{\kappa}$. In the numerical example considered, $\ensuremath{\kappa}$ is about 0.22 and the cancellation goes something like +14 MeV-15 MeV=-1 MeV. These findings, when juxtaposed with the standard Brueckner results for the simple models in question, suggest that a departure from the standard prescription of hole and particle energies in reaction-matrix theory may be necessary when $\ensuremath{\kappa}$ is sizeable-as in liquid $^{3}\mathrm{He}$ and the high-density neutron gas, as well as equilibrium nuclear matter described with some potentials.

Mitchel Weissbluth