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arXiv:cond-mat/9411012

A nonperturbative microscopic theory of Hamiltonian lattice gauge systems

R. F. Bishop, NEIL J. DAVIDSON, Yang Xian

Published Nov 2, 1994• 0 citations
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Abstract

A review is given of our recent application of a systematic microscopic formulation of quantum many-body theory, namely the coupled-cluster method (CCM), to Hamiltonian $U(1)$ lattice gauge models in the pure gauge sector. It is emphasized that our CCM results represent a natural extension or resummation of the results from the strong-coupling perturbation theory.

DOI
10.48550/arxiv.cond-mat/9411012

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A review is given of our recent application of a systematic microscopic formulation of quantum many-body theory, namely the coupled-cluster method (CCM), to Hamiltonian U(1)U(1)U(1) lattice gauge models in the pure gauge sector. It is emphasized that our CCM results represent a natural extension or resummation of the results from the strong-coupling perturbation theory.
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The coupled cluster method (CCM) is one of the most powerful and most successful fully microscopic, ab initio formulations available for quantum N-body theory, with N finite or infinite. It has probably been applied to more systems in quantum chemistry, nuclear, condensed matter and other areas of physics, and quantum field theory than any other competing method. In nearly all such cases the numerical results are either the best or among the best available. The CCM can deal with ground- and excited-state energies of closed- and open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from imbedding linear response theory within it. Extensions exist to deal with systems at nonzero temperature and out of equilibrium. At the formal level it provides an exact mapping of the quantum-mechanical problem onto a classical Hamiltonian phase space where the multiconfigurational canonical classical coordinates have specific cluster and locality properties. In this way it can provide exact hierarchical generalizations of mean-field theory and the random phase approximation. We discuss here both the formalism itself and a selection of its applications.