Theory Seminar

Sattwik Deb Mishra (Stanford University):
We describe a procedure to approximate the long stroboscopic-time average of observables for isolated periodically-driven quantum many-body systems.

Sattwik Deb Mishra (MPQ)
Group seminar via zoom
Wed, 26 January 2022, 17:00 pm (MEZ)

Abstract:

We describe a procedure to approximate the long stroboscopic-time average of observables for isolated periodically-driven quantum many-body systems. Our procedure builds upon recently developed filtering techniques in the context of isolated systems with time-independent Hamiltonians. The long stroboscopic-time average of an observable is its expectation value in the Floquet diagonal ensemble, i.e., the density operator that is diagonal in the basis of the Floquet eigenstates with the diagonal elements being the squared overlaps of the initial state with the eigenstates. We approximate the diagonal ensemble by a filtered state obtained by the action of a Gaussian filter operator on the initial state. We show that expectation values in the filtered state can be calculated, without its explicit construction, using periodic observations of the driven system. We demonstrate the filtering procedure using tensor network dynamical simulations of a periodically-driven spin chain and show that the filtered expectation value converges to the diagonal ensemble value with decreasing filter width. Furthermore, we observe that the convergence behaviour of the filtered expectation value also provides a clear signature of the Floquet dynamical phenomenon of prethermalization.