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. Using the method of Monte Carlo with importance sampling, we construct a stochastic basis of Bargmann link states, drawn from a physical probability density function. In the next step, we compute transition amplitudes between stochastic basis states. Then, we extract energy spectra and wave functions from a matrix of transition elements. To test this method, we apply it to U(1) lattice gauge theory in (2+1) dimensions and compute the energy spectrum, wave functions and thermodynamic functions of the electric Hamiltonian of this theory. We compare the numerical results with the analytical results and observe a reasonable scaling of energies and wave functions in the variable of time.
SPECTRUM AND WAVE FUNCTIONS OF U(1)2+1 LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN