Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits

Understand

We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e.

• single-site operators which, up to a phase, are simply shifted by the time evolution.
• We classify all circuits allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons.
• Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly.