Information Bounds on phase transitions in disordered systems

Abstract: Information theory, rooted in computer science, and many-body physics, have traditionally been studied as (almost) independent fields. Only recently has this paradigm started to shift, with many-body physics being studied and characterized using tools developed in information theory. In our work, we introduce a new perspective on this connection, and study phase transitions in models with randomness, such as localization in disordered systems, or random quantum circuits with measurements. Utilizing information-based arguments regarding probability distribution differentiation, we bound critical exponents in such phase transitions (specifically, those controlling the correlation or localization lengths). We benchmark our method and rederive the well-known Harris criterion, bounding critical exponents in the Anderson localization transition for noninteracting particles, as well as classical disordered spin systems. We then move on to apply our method to many-body localization. While in real space our critical exponent bound agrees with recent consensus, we find that, somewhat surprisingly, numerical results on Fock-space localization for limited-sized systems do not obey our bounds, indicating that the simulation results might not hold asymptotically (similarly to what is now believed to have occurred in the real-space problem). We also apply our approach to random quantum circuits with random measurements, for which we can derive bounds transcending recent mappings to percolation problems.