A derivation of the pairing-correlation method

Michel Baranger

A variational approach to the ground state of a many-fermion system is developed with the trial function of condensed pairs proposed by Blatt. The calculation of matrix elements is done by a diagrammatic method which is much simpler than Blatt's. The method is susceptible of generalization to higher correlations. It is also shown that the theory is identical with Hartree-Bogolyubov theory. The Hartree-Bogolyubov equations are derived from the variational point of view.

C.H. Dasso, Abraham Klein, Wang-Keiser Ching-Yun +1 more

Xiaochuan Ren, Jingxiang Zou, Haodong Zhang +2 more

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n -block ( n = 1–4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.

J. Bang, Joachim Krumlinde

Tohru Morita

A general discussion on applying the cluster variation method to non-uniform Ising and Heisenberg models is given. In particular, a general formula is provided for obtaining the linear response to increases of the external fields and the parameters of interactions for the uniform Ising and Heisenberg models in the cluster variation method. As an illustration, it is shown that the expressions of the spin-pair correlation function in the pair and the square approximation are readily derived by the formula, for the Ising models on the square and simple cubic lattices.