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 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) SU(2) gauge symmetry as quantum group, i.e., 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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Acknowledgments
The numerical calculations were carried out on cluster computers at iTHEMS in RIKEN. This work was supported by JSPS KAKENHI Grant Numbers 21H01007, and 21H01084.
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Hayata, T., Hidaka, Y. String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory. J. High Energ. Phys. 2023, 126 (2023). https://doi.org/10.1007/JHEP09(2023)126
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DOI: https://doi.org/10.1007/JHEP09(2023)126