Extension of the coupled-cluster method: A variational formalism

A general quantum many-body theory in configuration space is developed by extending the traditional coupled-cluster method (CCM) to a variational formalism. Two independent sets (destruction and creation sets) of distribution functions are introduced to evaluate the Hamiltonian expectation. An algebraic technique for calculating these distribution functions via two self-consistent set of equations is given. By comparing with the traditional CCM and with Arponen's extension, it is shown that the former is equivalent to a linear approximation to one set of distribution functions and the latter is equivalent to a (generalized) random-phase approximation to it. In addition to these two approximations, other higher-order approximation schemes within the formalism are also discussed. As a demonstration, we apply this technique to a quantum antiferromagnetic spin model.