Phase bands for periodically driven integrable quantum systems

In this talk, we are going to chart out application of the adiabatic-impulse approximation method for addressing the properties of periodically driven integrable systems and show that this method provides us with a tool for analytic computation of the phase bands (eigenvalues of the time evolution operator) in the low drive frequency limit where the standard high frequency perturbative expansions fail. Using this method and another, more general,argument, we provide exact analytic conditions for crossings of hese  bands in these driven systems. We show that such crossings are related to change in topology of the driven systems and point out that the signature of these crossings can be found in a certain class of correlation functions of the model.