Development of Floquet Theory and Applications in Time Crystals

Abstract

Discrete time crystals are an emerging research topic in quantum many-body physics and con- densed matter. The concept of time translational symmetry breaking which governs discrete time crystals is an interesting topic of study. The system under study is the Aubry-Andre-Harper model which has been used along with discrete time crystal to involve some site-dependent quasiperiodicity in the time crystal. The process of Floquet driving is done to evolve the states to different times. Floquet driving technique is a widely used technique to study the dynamics of non-equilibrium systems. In the quasiperiodic time crystal, each spin is given a cosine modulated rotation(full-wave) at each cycle of rotation. When each spin is given the same rotation of π, the initial state repeats after two cycles and thus such a time crystal has time period twice that of the original system. Another protocol, where individual spins of the system is subjected to different but fixed rotations periodically, has been studied. Our initial results with this protocol shows certain signatures for realizing time crystals. However, confirmation of the same will require further studies.