Stability of Periodically Driven Topological Phases against Disorder

Oles Shtanko, Ramis Movassagh

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases.

GAO Ming-Jian, MA Yu-peng, AN Jun-Hong

Israel Klich

Oles Shtanko, Ramis Movassagh

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These non-equilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder that is also seen at equilibrium. However, the existence of topological stability under a general setting is an open problem. We propose an effective theory that leverages on modern free probability theory and ideas in random matrices to analytically capture the existence of the topological phase for finite driving frequencies and across a range of disorder. We predict that, depending on the strength of disorder, such systems may be gapped (topological) or gapless (trivial). The theory can be used to predict properties of the transition between the two phases including the critical point. We corroborate our results by comparing to exact diagonalization for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang (BHZ) models.

Roderich Moessner, Joel E. Moore

Ion Cosma Fulga, Mykola Maksymenko, Maria-Theresa Rieder +2 more

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 many-body 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.