Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

TL;DR

This paper introduces a novel stochastic basis method to compute excited state spectra and wave functions in lattice gauge theory, successfully applied to U(1)_{2+1} with results matching analytical predictions.

Contribution

The paper presents a new stochastic basis approach for calculating spectra and wave functions in lattice gauge theories, including initial results for the full Hamiltonian.

Findings

Excellent agreement with analytical results for electric Hamiltonian

Scaling behavior observed in energies and wave functions

First results obtained for full Hamiltonian with magnetic term

Abstract

We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between stochastic basis states. From such transition matrix we extract wave functions and the energy spectrum. We apply this method to $U(1)_{2+1}$ lattice gauge theory. As a test we compute the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian and compare it with analytical results. We find excellent agreement. We observe 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.