Matthew Foster

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Non-equilibrium quantum many-body physics is in general very poorly understood. I will talk about recent developments understanding a new class of purely quantum particle dynamics with completely trivial kinetics. This is the physics of interacting fermions, monitored by external measurements. Inspired by previous work in the contexts of both random quantum circuits and monitored free-fermion dynamics, we use non-equilibrium field theory to craft a framework to detect phase transitions in the entanglement for such a system. The theory takes a form that is very similar to the single-particle theory of Anderson localization: a replicated nonlinear sigma model. I will explain how interactions introduce anisotropy in the geometry of the sigma model. The most prominent part is a "mass term" that we identify with the Fermi's golden rule of rate density of particle scattering. Such a rate density should vanish in the "area-law" phase, where entanglement is suppressed by the measurements. Our framework allows us to draw important implications from this for the nature of the entanglement phase transition. I will summarize how the analysis can be applied to different Altland-Zirnbauer classes of monitored dynamics, and how the "shape" of the entanglement transition might be studied from the point of view of Ricci flow on the sigma model manifold.

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Rice University
InnoDom Cologne, Weyertal 109, 50931 Köln join online
Contact: Sebastian Diehl, Simon Trebst