Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

Speaker: Mohit Pandey, Boston University, Physics Department

When: December 11, 2020 (Fri), 01:00PM to 02:00PM (add to my calendar)

This event is part of the Departmental Seminars.

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work [1], we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from integrable to chaotic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

[1] https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041017

PhD Dissertation Committee: Profs. Liam Fitzpatrick (Chair), David K Campbell (First Reader), Anatoli Polkovnikov (Second Reader) , Alex Sushkov, and Pankaj Mehta.

Zoom link: https://bostonu.zoom.us/j/93353466732?pwd=ZDJ2RENnaHdOYXhkSDJaVmFUZXljZz09

Meeting ID: 933 5346 6732

Passcode: 234795