About The Speaker
Joaquin Rodriguez-Nieva is a condensed matter theorist with interests in many-body quantum dynamics, non-equilibrium statistical physics, and quantum sensing. His academic training was done at MIT working on the physics of two-dimensional materials under the supervision of Millie Dresselhaus and Leonid Levitov. He then moved to Harvard University to work in the groups of Eugene Demler and Mikhail Lukin, and then to Stanford University as a Moore postdoctoral fellow. He is currently an assistant professor in the department of physics at Texas A&M.
The emergence of statistical mechanics in isolated quantum many-body systems has been a topic of foundational interest since the birth of quantum mechanics. Unlike classical systems, notions of chaos and ergodicity in many-body quantum systems still remain ill-defined. For this reason, designing quantitative measures of quantum chaos are of fundamental importance. One widely-accepted definition is through the random matrix behavior of Hamiltonian eigenstates. In this talk, I will introduce an eigenstate metric for quantum chaos that quantifies the distance between the microcanonical distribution of entanglement entropy produced by eigenstates and that produced by pure random states with appropriate constraints. We find that, for chaotic systems, the distribution of entanglement entropy of eigenstates deviates from random matrix theory predictions for all models and systems sizes studied. In particular, we show that the variance of the microcanonical entanglement entropy distribution of eigenstates is an extremely sensitive probe of quantum chaos. I will show numerical results in a variety of physical Hamiltonians having both chaotic and integrable limits as well as Floquet systems with and without randomness. When employing our metric of chaos in Hamiltonian systems known to exhibit strongly chaotic behavior, we find that deviations from random matrix behavior are negligible only in small pockets of parameter space. This suggests that maximally chaotic Hamiltonians, those with eigenstates exhibiting random matrix behavior, exist only in fine-tuned regions of parameter space.