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Theoretical and Mathematical Physics

Cluster generalization of the coherent-potential approximation on the basis of the projection formalism in an augmented space

А. К. Аржников, S. G. Novokshonov

Published Jul 1, 1990• 1 citation
Publisher
DOI
10.1007/bf01017202

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We apply the homomorphic cluster coherent potential approximation (HCPA) to systems with site-diagonal and/or off-diagonal randomness. We show numerically that the average Green's function obtained on the basis of the HCPA is analytic off the real axis on the complex energy plane. We also show that the HCPA reproduces the ordinary single-site CPA and the molecular CPA when systems include only diagonal disorder. The HCPA is advantageous in that it can deal with both site-diagonal and off-diagonal disorder in a unified manner. We also present a numerical result for a disordered chain by taking both kinds of disorder into account. The density of states calculated in the HCPA is in good agreement with the result of a computer simulation.
We develop a general quantum many-body theory in configuration space by extending the traditional coupled-cluster method to a variational formalism. A set of distribution functions are introduced to evaluate the expectation value of the Hamiltonian. An algebraic technique for calculations of these distribution functions via a set of self-consistent set of equations is given. As a demonstration, we apply this method to a quantum antiferromagnetic spin model. It is shown that one of the lowest-order approximations within this new technique agrees with the traditional coupled-cluster method. Comparison with the method of correlated basis functions is also made.
A particle-hole formalism is defined which is consistent with the tensor notation (and the index pairing) of the generators of the unitary group and their many-particle generalization. The corresponding generalized Wick theorem is formulated. The classification of basis operators as ‘‘closed,’’ ‘‘open,’’ ‘‘closed from above,’’ and ‘‘closed from below’’ given previously is extended to the present context. Both the perturbative and nonperturbative construction of effective Fock space Hamiltonians is discussed in the particle-hole formalism, especially for the case that the ‘‘physical vacuum’’ satisfies a Hartree–Fock condition. For the calculations of the correlation energy of the physical vacuum Cizek’s CP-MET is compared formally with the unitary variant, the UNICEP (unitary coupled electron pair) approximation. A simple derivation of Goldstone’s ‘‘linked-cluster expansion’’ is also given.