Eigenstate Order in Floquet Systems

Martin Reitter

Sthitadhi Roy, Achilleas Lazarides

Localization-protected quantum order extends the idea of symmetry breaking and order in ground states to individual eigenstates at arbitrary energy. Examples include many-body localized static and $\ensuremath{\pi}$ spin glasses in Floquet systems. Such order is inherently dynamical and difficult to detect as the order parameter typically varies randomly between different eigenstates, requiring specific superpositions of eigenstates to be targeted by the initial state. We show that two-time correlators overcome this, reflecting the presence or absence of eigenstate order even in fully mixed, infinite temperature states. We show how spatiotemporal correlators are generated by the recently introduced dynamical potentials, demonstrating this explicitly using an Ising spin glass and a Floquet $\ensuremath{\pi}$ spin glass and focusing on features mirroring those of equilibrium statistical mechanics such as bimodal potentials in the symmetry-broken phase.

Roderich Moessner, Shivaji L. Sondhi

Tatsuhiko N. Ikeda, Koki Chinzei, Hirokazu Tsunetsugu

By using the Floquet eigenstates, we derive a formula to calculate the high-order harmonic components of the electric current (HHC) in the setup where a monochromatic laser field is turned on at some time. On the basis of this formulation, we study the HHC spectrum of electrons on a one-dimensional chain with a staggered potential to study the effect of multiple sites in the unit cell such as the systems with charge density wave order. With the help of the solution for the Floquet eigenstates, we analytically show that two plateaus of different origins emerge in the HHC spectrum. The widths of these plateaus are both proportional to the field amplitude, but inversely proportional to the laser frequency and its square, respectively. We also show numerically that multistep plateaus appear when both the field amplitude and the staggered potential are strong.

J.V. Hern 'andez, Yujun Wang, Brett D. Esry

Jayendra N. Bandyopadhyay, Jiao Wang, Jiangbin Gong

The Floquet spectra of a class of driven SU(2) systems have been shown to display butterfly patterns with multifractal properties. The implication of such critical spectral behavior for the Floquet eigenstate statistics is studied in this work. Following the methodologies for understanding the fractal behavior of energy eigenstates of time-independent systems on the Anderson transition point, we analyze the distribution profile, the mean value, and the variance of the logarithm of the inverse participation ratio of the Floquet eigenstates associated with multifractal Floquet spectra. The results show that the Floquet eigenstates also display fractal behavior but with features markedly different from those in time-independent Anderson-transition models. This motivated us to propose random unitary matrix ensemble, called "power-law random banded unitary matrix" ensemble, to illuminate the Floquet eigenstate statistics of critical driven systems. The results based on the proposed random matrix model are consistent with those obtained from our dynamical examples with or without time-reversal symmetry.