Topology and localization of a periodically driven Kitaev model

Abstract

Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be manybody localized, which implies that they are stable and do not heat up as a result of the driving. What types of anomalous topological phenomena can be stabilized in driven systems, and in particular, can an anomalous phase exhibiting non-Abelian anyons be stabilized? We address this question using an exactly solvable, stroboscopically driven 2D Kitaev spin model, in which anisotropic exchange couplings are boosted at consecutive time intervals. The model shows a rich phase diagram which contains anomalous topological phases. We characterize these phases using weak and strong scattering-matrix invariants defined for the fermionic degrees of freedom. Of particular importance is an anomalous phase whose zero flux sector exhibits fermionic bands with zero Chern numbers, while a vortex binds a pair of Majorana modes, which as we show support non-Abelian braiding statistics. We further show that upon adding disorder, the zero flux sector of the model becomes localized. However, the model does not remain localized for a finite density of vortices. Hybridization of Majorana modes bound to vortices form "vortex bands", which delocalize by either forming Chern bands or a thermal metal phase. We conclude that while the model cannot be many-body localized, it may still exhibit long thermalization times, owing to the necessity to create a finite density of vortices for delocalization to occur.

Crossdimensional universality classes in static and periodically driven Kitaev models

“…4(c) and 4(d)]. This is consistent with previous works dealing with similar driving protocols [36,77]. In Appendix B, we present a detailed analysis of the edge modes in each phase.…”

“…Because these modes appear as floating bands within the gap, their topological invariant W 0 cancels out. Analogous edge modes representing a weak topological phase and protected by particle-hole and translation symmetry were observed for similar driving schemes [77]. Static counterparts of such floating band modes were shown to lead to second-order topological superconducting states in the presence of s ± -wave superconductivity [105].…”

“…(22) in the strong driving limit J = 1 and fixed T was shown to lead to radical chiral Floquet phases characterized by excitations with fractional statistics [36]. Another work [77] analyzed a different four-step modulation and the stability of the chiral MMs with respect to disorder.…”

“…The three-step driving protocol inherently generates chiral Majorana modes propagating along the edges of a sample with finite size [36,77,81]. To verify this, we analyze semi-infinite strips with both armchair and zigzag edges and calculate the quasienergy spectrum and the corresponding eigenmodes as a function of the (one-dimensional) momentum k defined for the infinite direction.…”

Floquet engineering multi-channel Kondo physics

“…Its application to correlated materials is particularly intriguing. In frustrated magnets, Floquet engineering * vquito@iastate.edu can theoretically tune the underlying exchange interactions [40][41][42][43][44][45][46][47][48][49][50] and induce chiral fields [51] by tuning the frequency, amplitude and polarization of the light. Previous applications of Floquet to Kondo systems include tuning topological Kondo insulators [28], inducing eta pairing [52] and driving dynamical phase transitions in the quarter-filled single-channel case [53].…”