Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions

We test the eigenstate thermalization hypothesis (ETH) in 1+1-dimensional SU(2) lattice gauge theory (LGT) with one flavor of dynamical fermions. Using the loop-string-hadron framework of the LGT with a bosonic cut-off, we exactly diagonalize the Hamiltonian for finite size systems and calculate matrix elements (MEs) in the eigenbasis for both local and non-local operators. We analyze different indicators to identify the parameter space for quantum chaos at finite lattice sizes and investigate how the ETH behavior emerges in both the diagonal and off-diagonal MEs. Our investigations allow us to study various time scales of thermalization and the emergence of random matrix behavior, and highlight the interplays of the several diagnostics with each other. Furthermore, from the off-diagonal MEs, we extract a smooth function that is closely related to the spectral function for both local and non-local operators. We find numerical evidence of the spectral gap and the memory peak in the non-local operator case. Finally, we investigate aspects of subsystem ETH in the lattice gauge theory and identify certain features in the subsystem reduced density matrix that are unique to gauge theories.