THE ENSEMBLE PROJECTOR MONTE CARLO METHOD: STUDYING THE U(1) LATTICE GAUGE THEORY WITH FERMIONS IN (2+1)-DIMENSIONS
J. Ranft · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2022
The ensemble projector Monte Carlo method is a lattice Monte Carlo method for studying gauge theories with and without Fermions in the Hamiltonian formulat ion.We study the compact U(1) lattice gauge theory with fermions in d = 2 + 1 dimensions.There are matrix elements with positive and negative signs in lattice gauge theories with fermions.As in the case of the Schwinger model, we find the energy expectation values calculated from matrix elements -using the two subsets of configurations with total positive and negative score to agree within the statistical errors to each other as well as to the energy expectation value calculated from average scores.We conclude that this method, which was previously only used in d = 1 + 1 dimensions can indeed be applied to lattice gauge theories with fermions in more than one spatial dimensions.