Out-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain

Abstract

We consider the dynamics of an XY spin chain subjected to an external transverse field which is periodically quenched between two values. By deriving an exact expression of the Floquet Hamiltonian for this out-of-equilibrium protocol with arbitrary driving frequencies, we show how, after an unfolding of the Floquet spectrum, the parameter space of the system is characterized by alternations between local and non-local regions, corresponding respectively to the absence and presence of Floquet resonances. The boundary lines between regions are obtained analytically from avoided crossings in the Floquet quasi-energies and are observable as phase transitions in the synchronized state. The transient behaviour of dynamical averages of local observables similarly undergoes a transition, showing either a rapid convergence towards the synchronized state in the local regime, or a rather slow one exhibiting persistent oscillations in the non-local regime, where explicit decay coefficients are presented.

Dynamical signatures of topological order in the driven-dissipative Kitaev chain

“…Aside from the anomalous transitions described above, the phase diagram of the drivendissipative Kitaev chain (as shown in Figure 6) has the same rib structure of Floquet resonances that appears in previous work [8,24,45]. The total number of edge modes, given by |ν 0 | + |ν π |, corresponds to that found by [45].…”

“…As we further increase T , we first encounter a finite intermediate region with broken AUS, after which the gap reopens and the first Floquet resonance occurs. This phase is characterized by avoided crossings of the quasi-rapidity bands and nonlocal hopping in the effective generator of (stroboscopic) time evolution [24]. According to the bulk-boundary correspondence, if we were to use OBC, an edge mode would be present inside the reopened gap.…”

“…2, there are new transitions induced by Floquet resonances. Such resonant regimes are characterized by long-range order [8], nonlocal Floquet Hamiltonians [24] and the possibility of high winding numbers [45].…”

“…Finally, in Section 4, periodic driving is added to the system. In this case, the behavior of the system becomes even more complex as a consequence of Floquet resonances [24]. For example, one can now have a seemingly unlimited number of edge modes, which are split into two types [25,26].…”

“…k) = e −iθ(k) cos * ξ(k) (k) = −e −iθ(k) sin * ξ(k) such that v * i • u j = δ ij .The two winding numbers(24) associated with these bands are:|q(k)| 2 − 4g 2 ∆ 2 ∂θ ∂k dk .…”