Triggering boundary phase transitions through bulk measurements in two-dimensional cluster states

We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements using tensor network methods. The state is subjected to uniform measurements M=cosθZ+sinθX on the lower boundary qubits and in all bulk qubits. Our results show that the boundary of the system exhibits volume-law entanglement at the measurement angle θ=π/2 and area-law entanglement for any θ