Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
| Autor: | Kan, Angus, Funcke, Lena, Kühn, Stefan, Dellantonio, Luca, Zhang, Jinglei, Haase, Jan F., Muschik, Christine A., Jansen, Karl |
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| Rok vydání: | 2021 |
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| Zdroj: | Phys. Rev. D 104, 034504 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.104.034504 |
| Popis: | 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. Comment: 13 pages, 3 figures; close to journal version |
| Databáze: | arXiv |
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