Hamiltonian lattice gauge theory: wavefunctions on large lattices

Abstract

We discuss an algorithm for the approximate solution of Schrödinger'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 10 × 10 × 10 lattice. The Hamiltonian matrix on the basis is sparse, and the elements can be calculated rapidly. The lowest eigenstates of the system are rapidly calculable.