Fig. 8: The operator related to the symmetry sectors of the ansatz state.
From: Quantum computing universal thermalization dynamics in a (2 + 1)D Lattice Gauge Theory
Because of the (remaining) Gauss laws, some operators outside of the subsystem are identical to operators within its complement. The operator shown, and a similar operator placed on the other boundary, commutes with all other operators in the BW-inspired ansatz shown in Fig. 7. Therefore, their (common) eigenspace are the symmetry sectors of the reduced density matrix.
