Two dimensional kicked quantum Ising model: dynamical phase transitions

TL;DR

This study investigates the ergodic and chaotic properties of a two-dimensional quantum Ising model under periodic driving, revealing complex relationships between spectral features and local observable ergodicity.

Contribution

It demonstrates that level spacing distribution aligns with random matrix theory across most parameters, challenging traditional links between spectral statistics and ergodicity.

Findings

Transitions between ordered and chaotic phases were observed.

Level spacing distribution matches Wigner surmise in most cases.

Spectral density flatness does not always indicate ergodicity.

Abstract

Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a $\delta$-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density and (ii) level spacing distribution of the Floquet quasienergy spectrum, as well as (iii) time-averaged autocorrelation function of components of the magnetization. Varying the parameters of the model, we found transitions between ordered (non ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density {\em do not} correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found nice agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially noninteracting, even in the regions where local observables are not ergodic or where spectral density is non-flat. These findings put in question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality.