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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Coupled cluster analysis of the U(1) lattice gauge model using a correlated "mean-field" reference state

S. J. Baker, R. F. Bishop, NEIL J. DAVIDSON

Published Mar 1, 1996• 19 citations
Publisher

Abstract

We apply the coupled cluster method (CCM) to the U(1) lattice gauge model in 2+1 dimensions, basing our analysis on a reference state which already contains a certain class of single-plaquette correlations, the so-called "mean-field" reference state. We consider the simplest possible approximation scheme for the coupled cluster calculation, in which only single-plaquette correlations are included. The use of the "mean-field" reference state allows us to reproduce, within this level of approximation, the correct leading-order behavior of the ground-state energy of the equivalent Mathieu problem in both the strong- and weak-coupling limits. In addition, we have calculated the mean plaquette and the odd- and even-parity mass gaps.

DOI
10.1103/physrevd.53.2610

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We apply the coupled cluster method (CCM) to the U(1) lattice gauge model in 2+1 dimensions, basing our analysis on a reference state which already contains a certain class of single-plaquette correlations, the so-called "mean-field" reference state. We consider the simplest possible approximation scheme for the coupled cluster calculation, in which only single-plaquette correlations are included. The use of the "mean-field" reference state allows us to reproduce, within this level of approximation, the correct leading-order behavior of the ground-state energy of the equivalent Mathieu problem in both the strong- and weak-coupling limits. In addition, we have calculated the mean plaquette and the odd- and even-parity mass gaps.
An ab initio formulation of microscopic quantum many-body theory, namely, the coupled-cluster method (CCM), is applied to the lattice gauge models, Z(2)Z(2)Z(2) in 2+1 dimensions, and U(1) in 1+1 and 2+1 dimensions. Both mode-mode couplings and plaquette-plaquette correlations are considered. In particular, within the one-plaquette approximation for the U(1) model, the CCM is able to include mode couplings of arbitrarily high order. It therefore reproduces essentially the exact numerical results for the equivalent Mathieu problem. These include the ground-state, plaquette, and excitation energies as functions of the coupling constant. Two-plaquette equations are solved by local approximations for both the U(1) and Z(2)Z(2)Z(2) models, and the results are impressive. Detailed comparisons with other methods, particularly perturbation theory, are made and discussed, with emphasis on the nonperturbative nature of the problem.
The coupled-cluster method (CCM) is applied to anisotropic-quantum-antiferromagnetic models in one and two dimensions (1D and 2D). Several hierarchical approximation schemes of the CCM are defined, which are specialized for the spin-lattice models. Good results are obtained for both ground-state and excited-state energies. The spin-spin correlation functions and the staggered magnetizations are also calculated. We have found that the CCM gives a qualitatively correct description of the entire Heisenberg-Ising phase, including the critical point where a phase transition occurs in 1D. Some interesting differences between 1D and 2D models near the critical point are discussed.
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J 1 – J 2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.
The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is largely due to the application of computational techniques that allow the method to be applied to high orders of approximation using a localized scheme known as the LSUBm scheme. A hitherto unreported aspect of this scheme is that results for LSUBm expectation values behave in distinctly different ways with odd and even values of m. Here, we consider the behavior of ground-state expectation values of odd and even orders of the CCM LSUBm approximation for unfrustrated spin-half Heisenberg antiferromagnets on the square and honeycomb lattice and the frustrated spin-half Heisenberg antiferromagnet on the triangular lattice. We demonstrate that results for odd and even orders of approximation show qualitatively different behavior for both the ground-state energy and the sublattice magnetization. Indeed, the odd series consistently forms an upper branch of results, and the even series a lower branch with respect to both ground-state energy and sublattice magnetization, for all of the models considered here.