Description
We analyze the entanglement structures of states produced in 1D monitored circuits where local Clifford unitaries are interspersed with single-site measurements. In the volume law phase, the average entanglement depth scales linearly with system size. Curiously, we continue to see long-range entanglement within the area law phase as well. At the critical point and in the area law phase, the entanglement depth scales with system size as a power law with an exponent between 0 and 1. We further calculate the fractal dimension of the largest cluster of entangled qubits within the state. We find that there is self similarity and the largest clusters have fractal dimensions between 0 and 1 in the area law phase.
This fractal dimension continuously goes to zero as the measurement probability approaches 1. Within the volume law phase, the fractal dimension of such clusters is 1.
