Excited States of U(1)$_{2+1}$ Lattice Gauge Theory from Monte Carlo Hamiltonian

TL;DR

This paper introduces a Hamiltonian-based Monte Carlo method using a stochastic basis to compute excited states and wave functions in U(1)$_{2+1}$ lattice gauge theory, validated against analytical results.

Contribution

It proposes a novel stochastic basis approach for Hamiltonian lattice gauge theory to efficiently compute spectra and wave functions of excited states.

Findings

Successful computation of energy spectra and wave functions for the electric Hamiltonian.

Reasonable scaling observed in energies and wave functions with respect to time.

Initial results obtained for the full Hamiltonian including magnetic terms on small lattices.

Abstract

We address an old problem in lattice gauge theory - the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge theory. We test the method by computing the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian of this theory and compare them with analytical results. We observe a reasonable scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.