Seminar by Dr. Roopayan Ghosh, UCL, London
Event Date: 
Wednesday, 8 February 2023 - 4:00pm

Title: Floquet perturbation Theory and a few applications

Speaker: Dr. Roopayan Ghosh, UCL, London

Zoom Link: https://zoom.us/j/92600161293?pwd=TjN3azB5ek5iMHBmUXRiOW1heU0rQT09

Abstract: The information of stroboscopic time evolution of quantum system described by a time-periodic Hamiltonian is encoded in the Floquet Hamiltonian HF . Among the different numerical and analytical techniques to calculate HF, I shall focus on Floquet Perturbation Theory (FPT) and discuss its regime of applicability and efficacy. To do so, I shall compute HF for weakly interacting fermions subjected to a continuous periodic drive using FPT, taking the interaction amplitude to be the perturbation parameter. I shall compare the Fidelity of the wavefunction obtained from FPT with exact numerics and Magnus expansion results to show that FPT gives significantly better results than Magnus expansion in the intermediate frequency regime. I also show that the perfect stroboscopic dynamical localization at all frequencies in the non-interacting model becomes a crossover of the steady states in the interacting model for the drive considered. Then, as further examples I shall briefly discuss how FPT captures localization transitions and multifractal states for the driven Aubry Andre model and conclude with how it was used to understand dynamical quantum scars in PXP chains.

References: 1. Floquet perturbation theory for periodically driven weakly interacting fermions,Roopayan Ghosh, Bhaskar Mukherjee, and K. Sengupta,Phys. Rev. B 102, 235114 – Published 4 December 2020.

2. Mobility edge and multifractality in a periodically driven Aubry-André model, Madhumita Sarkar, Roopayan Ghosh, Arnab Sen, and K. Sengupta, Phys. Rev. B 103, 184309 – Published 21 May 2021.

3. Signatures of multifractality in a periodically driven interacting Aubry-André model, Madhumita Sarkar, Roopayan Ghosh, Arnab Sen, and K. Sengupta, Phys. Rev. B 105, 024301 – Published 3 January 2022.

4.Collapse and revival of quantum many-body scars via Floquet engineering, Bhaskar Mukherjee, Sourav Nandy, Arnab Sen, Diptiman Sen, and K. Sengupta, Phys. Rev. B 101, 245107 – Published 1 June 2020

Venue: 
Zoom
IIT Bombay, Powai, Mumbai