Hamiltonian lattice gauge theory: wavefunctions on large lattices

TL;DR

This paper presents an algorithm for approximating solutions to Schrodinger's equation in lattice gauge theory, specifically for SU(3), enabling the calculation of low-energy eigenstates on large lattices.

Contribution

It introduces a basis generation method using an effective Hamiltonian, allowing efficient computation of eigenstates in large lattice gauge systems.

Findings

Basis with about 10^4 states on a 10x10x10 lattice

Sparse Hamiltonian matrix with rapidly calculable elements

Low eigenstates are readily computable

Abstract

We discuss an algorithm for the approximate solution of Schrodinger's equation for lattice gauge theory, using lattice SU(3) as an example. A basis is generated by repeatedly applying an effective Hamiltonian to a ``starting state.'' The resulting basis has a cluster decomposition and long-range correlations. One such basis has about 10^4 states on a 10X10X10 lattice. The Hamiltonian matrix on the basis is sparse, and the elements can be calculated rapidly. The lowest eigenstates of the system are readily calculable.