P. Schindler Geometric Floquet Theory
- Starts: 12:00 pm on Friday, December 13, 2024
- Ends: 1:30 pm on Friday, December 13, 2024
Periodic driving has become crucial in quantum simulation and sensing, and has led to a new paradigm of non-equilibrium order in condensed matter. Our present-day understanding of periodically driven systems is based on the Floquet theorem, which guarantees the existence of a rotating reference frame in which the system is described by a time-independent, so-called, Floquet Hamiltonian.
Despite significant advancements, numerous open questions persist. For instance, computing the Floquet Hamiltonian is notoriously hard, and the absence of a variational principle limits approximation techniques. Moreover, the quasi-energies of the Floquet Hamiltonian are ambiguous, precluding the unique definition of a Floquet ground state.
In this talk, I introduce a geometric formulation of Floquet theory.
We establish a duality between periodically driven systems and transitionless counterdiabatic driving, which paves the way for formulating a variational principle for the Floquet Hamiltonian.
Moreover, we can identify quasienergy folding as a consequence of an incomplete gauge-fixing $U(1) \mapsto \mathbb{Z}$.
This allows us to introduce a unique gauge-fixing based on inherently gauge-invariant quantities, which decomposes the dynamics into a purely geometric and a purely dynamical evolution. The dynamical average-energy operator provides an unambiguous sorting of the quasienergy spectrum, as I will demonstrate on an exactly solvable two-level system, and a non-integrable kicked Ising chain. Moreover, I will show that the geometric contribution accounts for inherently nonequilibrium effects—like the $\pi$-quasienergy gap in discrete time crystals or anomalous edge modes in anomalous Floquet topological insulators.
- Location:
- SCI 352
- Speaker
- Paul Schindler
- Institution
- Max Planck Instiitute
- Host
- Anatoli Polkovnikov