Multifractality in nonunitary random dynamics

We explore the multifractality of steady state wave function in non-unitary random quantum dynamics one dimension. focus on two classes systems: hybrid Clifford circuit model and free fermion dynamics. In model, we map measurement driven transition to an Anderson localization effective graph space by using properties stabilizer state. show that volume law phase with nonzero rate is non-ergodic exhibits weak multifractal behavior. apply same method automaton obtain similar phase. For system a critical state, compute moments probability distribution single particle demonstrate it also weakly has strong variations real space.