Investigating a (3+1) D topological θ -term in the Hamiltonian formulation of lattice gauge theories for quantum and classical simulations

Abstract

Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the (3+1)D topological θ-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way toward Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory with the θ-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of θ, as indicated by an avoided level crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed (3+1)D tensor network methods and quantum simulations, once sufficient resources become available.