Non-heating Floquet systems

Abstract

In the last decade there has been immense progress in experimentally realizing periodically driven, so-called Floquet systems, that exhibit topological features. However, there is an expectation that most Floquet systems heat up with time, absorbing energy from the drive, and thus evolve towards a featureless state in which all local correlations are fully random. In this thesis it is shown that it is theoretically possible to have a Floquet system which do not heat up, giving that any existing local correlations could be infinitely long lived. In other words, this shows that interesting physical phenomenon, such as a non-trivial topological phase, could in principal be present in a Floquet system for infinitely long times. The Floquet model which exhibits this non-heating phase is that of a square-wave drive where the Hamiltonian of the system jumps between an arbitrarily chosen CFT and a sine-square deformation of the same CFT. This model was first proposed in 2018 by Wen and Wu in Ref. [1]. We present in this thesis a generalization of the Floquet system proposed by Wen and Wu – we still use the same square wave drive but now with what we call a sine-k-square deformation, hence a deformation of higher harmonics. With this generalization we also find the interesting property of a non-heating phase for certain values of the driving parameters. Furthermore, we find that the value of k in the sine-k-squared deformation that we propose has some rather important implications for which driving parameter values we can have in a non-heating phase: The region of the driving parameter values which gives the non-heating phase shrinks with growing k.