Information and Physics: The Harris Criterion and Beyond

by Prof. Moshe Goldstein

Tel-Aviv University
at Physics Colloquium

Tue, 05 Mar 2024, 15:15
Ilse Katz Institute for Nanoscale Science & Technology (51), room 015


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. I will start by reviewing several such directions, ranging from Maxwell’s demon and information engines, through information bounds on renormalization group flows, to the black hole information paradox, then to bounds on classical and quantum glass annealing dynamics based on their computational complexity. I will then move forward to our own recent work, and bring a new perspective on this connection, studying phase transitions in models with randomness, such as localization in disordered systems, or random quantum circuits with measurements. Utilizing information-based arguments on probability distribution differentiation, we bound the critical exponents in such phase transitions. We benchmark our method and rederive the well-known Harris criterion, bounding the critical exponent in the Anderson localization transition for noninteracting particles, as well as in classical disordered spin systems, and then extend it to dynamical exponents. Moving forward to many-body localization, we infer bounds both on real space and Fock space localization critical exponents. Interestingly, our bounds are not obeyed by prior studies in several cases; some of our bounds are aligned with recent consensus, while some point to newly found problems in previously obtained numerical and analytical results. Additionally, we apply our method to measurement-induced phase transitions in random quantum circuits. To date, analytical results for such phase transitions have only been obtained for one-dimensional circuits with Haar-random unitary gates, using the zeroth Rènyi entropy as a marker of the phases. Our bounds are valid for arbitrary circuit dimensions, gate combinations, and phase markers, and are obeyed by existing numerical results.

Created on 08-01-2024 by Maniv, Eran (eranmaniv)
Updaded on 26-02-2024 by Maniv, Eran (eranmaniv)