Repeated quantum measurements can generate effective new nonequilibrium dynamics in matter. Here we combine such a measurement driven system with disorder. In particular, we investigate the diffusive behavior in the system and the effect of various types of disorder on the measurement induced chiral transport protocol. We begin by characterizing the diffusive behavior produced by the measurements themselves in a clean system. We then examine the edge flow of particles per measurement cycle for three different types of disorder: site dilution, lattice distortion, and disorder in on-site chemical potential. In the quantum Zeno limit, the effective descriptions for the disordered measurement system with lattice distortions and random on-site potential can be modeled as a classical stochastic model, and the overall effect of increasing these disorders induces a crossover from perfect flow to zero transport. On the other hand if vacancies are present in the lattice the flow of particles per measurement cycle undergoes a percolation phase transition from unity to zero with percolation threshold $p_c\approx 0.26$, with critical exponent $\nu \approx 1.35$. We also present numerical results away from Zeno limit and note that the overall effect of moving away from the Zeno effect is to reduce particle flow per cycle when the measurement frequency in our protocol is reduced.

• Received 2 August 2023
• Revised 26 October 2023
• Accepted 4 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.214305