3+1D $\theta$-Term on the Lattice from the Hamiltonian Perspective
| Autor: | Angus Kan, Lena Funcke, Stefan Kühn, Luca Dellantonio, Jinglei Zhang, Jan F. Haase, Christine A. Muschik, Karl Jansen |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
energy: ground state
High Energy Physics::Lattice topological [charge] gap Markov chain [Monte Carlo] density [charge] Monte Carlo: Markov chain High Energy Physics - Lattice strong coupling energy: density ddc:530 nonabelian numerical calculations ground state [energy] lattice Hamiltonian formalism lattice field theory critical phenomena crossing U(1) abelian Hamiltonian charge: density charge: topological network density [energy] |
| Zdroj: | Proceedings of Science / International School for Advanced Studies (LATTICE2021), 112 (2022). doi:10.22323/1.396.0112 38th International Symposium on Lattice Field Theory, Lattice 2021, Online, United States, 2021-07-26-2021-07-30 |
| DOI: | 10.22323/1.396.0112 |
| Popis: | 38th International Symposium on Lattice Field Theory, Lattice 2021, Online, United States, 26 Jul 2021 - 30 Jul 2021; Proceedings of Science / International School for Advanced Studies (LATTICE2021), 112 (2022). doi:10.22323/1.396.0112 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. Our numerical results reveal a novel phase transition at fixed values of $\theta$ in the strong-coupling regime. The transition is evidenced by an avoided level crossing in the ground state energy, as well as sudden changes in the plaquette expectation value, the electric energy density, and the topological charge density. Extensions of our work to larger lattices can be readily performed using state-of-the-art tensor network simulations. Moreover, our work provides a concrete starting point for an eventual quantum simulation of the $\theta$-dependent phase structure and dynamics of lattice gauge theories in 3+1D. This talk is mainly based on [1]. We expand beyond [1] by including a derivation of the (non-)Abelian fixed-length Higgs term in the Hamiltonian formulation for future studies of (non-)Abelian-Higgs models with a $\theta$-term. Published by SISSA, Trieste |
| Databáze: | OpenAIRE |
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