An ab initio formulation of microscopic quantum many-body theory, namely, the coupled-cluster method (CCM), is applied to the lattice gauge models, $Z(2)$ 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 $Z(2)$ 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.An ab initio formulation of microscopic quantum many-body theory, namely, the coupled-cluster method (CCM), is applied to the lattice gauge models, $Z(2)$ 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 $Z(2)$ 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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJul 15, 199334 citations

Hamiltonian Lattice Gauge Theories

Giovanni Cataldi

Graduate texts in physicsJan 1, 20260 citations

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

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.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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMar 1, 199619 citations

TOWARDS A COUPLED-CLUSTER TREATMENT OF SU (N) LATTICE GAUGE FIELD THEORY

R. F. Bishop, N.E. Ligterink, Niels R. Walet

A consistent approach to Hamiltonian SU (N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU (N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional.A consistent approach to Hamiltonian SU (N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU (N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional.

International Journal of Modern Physics BDec 15, 20065 citations

Phase transition in one-dimensional lattice gauge theories

Mohammad Khorrami

arXiv:hep-th/9412090International Journal of Theoretical PhysicsMar 1, 19961 citation

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)

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)

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.