The Shifted Coupled Cluster Method: A New Approach to Hamiltonian Lattice Gauge Theories

TL;DR

This paper introduces a novel shifted coupled cluster method adapted for Hamiltonian lattice gauge theories, enabling non-perturbative solutions for $SU(N)$ gauge models with improved truncation and gauge invariance handling.

Contribution

It develops a new shifted coupled cluster approach for Hamiltonian lattice gauge theories, allowing self-consistent solutions with cluster truncation and gauge invariance.

Findings

Successfully applied to $SU(2)$ in 3D space-time.

Provides a self-consistent solution to non-linear Schrödinger equations.

Demonstrates the method's potential for non-perturbative gauge theory analysis.

Abstract

It is shown how to adapt the non-perturbative coupled cluster method of many-body theory so that it may be successfully applied to Hamiltonian lattice $SU(N)$ gauge theories. The procedure involves first writing the wavefunctions for the vacuum and excited states in terms of linked clusters of gauge invariant excitations of the strong coupling vacuum. The fundamental approximation scheme then consists of i) a truncation of the infinite set of clusters in the wavefunctions according to their geometric {\em size}, with all larger clusters appearing in the Schr\"odinger equations simply discarded, ii) an expansion of the truncated wavefunctions in terms of the remaining clusters rearranged, or ``shifted'', to describe gauge invariant {\em fluctuations} about their vacuum expectation values. The resulting non-linear truncated Schr\"odinger equations are then solved self-consistently and exactly. Results are presented for the case of $SU(2)$ in $d=3$ space-time dimensions.