3+1D $\theta$-Term on the Lattice from the Hamiltonian Perspective

Understand

Quantum and tensor network simulations have emerged as prominent sign-problem free approaches to lattice gauge theories.

• Unlike conventional Markov chain Monte Carlo methods, they are based on the Hamiltonian formulation.
• In this talk, we fill a gap in the literature and present the first derivation of the Hamiltonian 3+1D $\theta$-term -- which is an important sign-problem afflicted term -- for Abelian and non-Abelian lattice gauge theories.
• Furthermore, we perform exact diagonalization for a 3+1D U(1) lattice gauge theory including the $\theta$-term on a unit periodic cube.