Ensemble projector Monte Carlo method, studying the lattice Schwinger model in the Hamiltonian formulation

The ensemble projector Monte Carlo method is a promising method to study lattice gauge theories with fermions in the Hamiltonian formulation. We study the massive Schwinger model and show that consistent results are obtained in the presence of positive and negative matrix elements. The expectation values for the average energy calculated from matrix elements with negative and positive scores, and calculated from the average scores, are consistent with each other and with results obtained from the local Hamiltonian Monte Carlo method. In contrast with the latter method, the ensemble projector Monte Carlo method can be also applied to gauge field theories in 2+1 and 3+1 dimensions.