String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory

• URL: http://arxiv.org/abs/2305.05950v2
• Date: Tue, 19 Sep 2023 05:42:10 GMT
• Title: String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory
• Authors: Tomoya Hayata, Yoshimasa Hidaka
• Abstract summary: We study the Hamiltonian lattice Yang-Mills theory based on spin networks. We study quantum scars in a nonabelian gauge theory.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on $\mathrm{SU}(2)$ Yang-Mills theory in $(2+1)$ dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the $q$ deformation, which respects the (discretized) $\mathrm{SU}(2)$ gauge symmetry as quantum group, i.e., $\mathrm{SU}(2)_k$, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)$_k$ and SU(3)$_k$ with naive cutoff and that based on the $q$-deformation to discuss cutoff dependence of the formulation.

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