Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations

• URL: http://arxiv.org/abs/2105.06019v2
• Date: Tue, 19 Oct 2021 01:03:39 GMT
• Title: Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
• Authors: Angus Kan, Lena Funcke, Stefan K\"uhn, Luca Dellantonio, Jinglei Zhang, Jan F. Haase, Christine A. Muschik, Karl Jansen
• Abstract summary: We derive the (3+1)D topological $theta$-term for Abelian and non-Abelian lattice gauge theories. We study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\theta$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards 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 $\theta$-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 $\theta$, 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.

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