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.
Highlights
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
We considered an anisotropic XY spin chain driven by a periodically-quenched external transverse field
Summary
The study of out-of-equilibrium systems has recently moved to the forefront of research in many-body physics, motivated largely by the desire to create interesting states of matter with properties beyond those achievable in equilibrium. Whereas all relevant properties of the periodic dynamics are encoded in the Floquet Hamiltonian, finding exact solutions remains a severe challenge, and these are usually limited to few-body systems This poses severe limitations to the application of Floquet theory when a large number of components are involved, as in condensed matter physics. A link is established between the locality of the Floquet Hamiltonian and the presence of avoided crossings between its eigenstates, which can be interpreted as Floquet resonances These resonances are generally not observable in the thermodynamic limit, but the free-fermionic nature of the model makes them visible in the single-particle spectrum, leading to a slow convergence of observables towards a synchronized state (i.e., the steady state of the stroboscopic time evolution [11,12]) with persistent oscillations in the non-local regime. The last section is reserved for conclusions and possible future avenues of research
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