Information theory bounds on randomness-based phase transitions. – (Noa Feldman / LPT / Seminar). – 10/09/2024, 14H

Noa Feldman(Université de Tel Aviv)

Seminar LPT, 10/09/2024, 14H, 3R1, seminar room, 3rd floor

Abstract :

We introduce a new perspective on the connection between many-body physics and information theory. We 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, rigorous results for bounds on critical exponents in such phase transitions are obtained with a minimal amount of work.
We first demonstrate our method by rederiving the well known Harris criterion, bounding \noareal-space and dynamical critical exponents in the Anderson localization transition.

We then move to obtain new bounds on critical exponents in many-body Fock space localization transition and localization in Coulomb-interactive models. Somewhat surprisingly, our bounds are not obeyed by previous studies of these systems, indicating possible inadequacies in their results, which we discuss. Finally, we apply our method to measurement-induced phase transition in random quantum circuits, obtaining bounds transcending recent mapping to percolation problems.

 

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