Theoritical study of driven correlated quantum matter

Periodically driven closed quantum many-body systems have become an active

field of research nowadays. The drive frequency, in such systems, is

an important parameter since it can be tuned to realize several interesting

phenomena that have no analog in equilibrium systems. A systematic theoretical

understanding of such phenomena has already been achieved in highfrequency

regime using inverse frequency perturbation expansions. These

kinds of expansion diverge in the low-frequency region where it is difficult

to find any semi-analytic techniques. The purpose of this thesis is to establish

a framework which works well for low to moderate drive frequencies.

Adiabatic-impulse approximation which we develop in this thesis provides

such a technique. We show that this method with proper modifications can

be successfully applied to describe many features of low-frequency phase diagram

of periodically driven non-interacting system like irradiated graphene in

frequency(ω
)-amplitude(A0) plane. We compute phase bands of such system

which are the eigenphases of corresponding time-evolution operator U(t, 0)

using adiabatic-impulse theory. We show that these results match extremely

well with exact numerical calculations in the low drive frequency region. We

also show that in systems like interacting bosons placed in a strong electric

field the phenomena of dynamic freezing can be enhanced by driving more

than one parameter of the Hamiltonian at some specific ratio of drive frequencies.

This phenomenon is understood as Stuckelberg interference of few

instantaneous energy levels in the many-body spectrum, undergoing exact

level crossing. We also study dynamics of driven systems in the presence of

stochastic resets. We find that such resets at random times result in a novel

steady value of reset averaged observables. On the other hand, stochastic

noise in the vector potential of an incident electromagnetic wave may drastically

change the phase band structure of irradiated systems at some specific

crystal momentum points in the Brillouin-zone. We numerically show that

self- averaging limit exists in such noisy dynamical systems and the modifications

in the phase band structure can be understood by analyzing the noise

averaged Hamiltonian.