SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis

• URL: http://arxiv.org/abs/2303.14264v3
• Date: Fri, 18 Aug 2023 18:09:20 GMT
• Title: SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis
• Authors: Xiaojun Yao
• Abstract summary: We consider the eigenstate thermalization hypothesis (ETH) for 2+1 dimensional SU(2) lattice gauge theory. We find energy level repulsion in momentum sectors with no remaining discrete symmetry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We test the eigenstate thermalization hypothesis (ETH) for 2+1 dimensional SU(2) lattice gauge theory. By considering the theory on a chain of plaquettes and truncating basis states for link variables at $j=1/2$, we can map it onto a quantum spin chain with local interactions and numerically exactly diagonalize the Hamiltonian for reasonably large lattice sizes. We find energy level repulsion in momentum sectors with no remaining discrete symmetry. We study two local observables made up of Wilson loops and calculate their matrix elements in the energy eigenbasis, which are shown consistent with the ETH.

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