Long Time Behaviour of a Local Perturbation in the Isotropic XY Chain Under Periodic Forcing

We study the isotropic XY quantum spin chain with a time-periodic transverse magnetic field acting on a single site. The asymptotic dynamics is described by a highly resonant Floquet–Schrödinger equation, for which we show the existence of a periodic solution if the forcing frequency is away from a discrete set of resonances. This in turn implies the state of the quantum spin chain to be asymptotically a periodic function synchronised with the forcing, also at arbitrarily low non-resonant frequencies. The behaviour at the resonances remains a challenging open problem.

Quantum correlated coherence and Hellinger distance in the critical systems

In this paper, we explore the quantum phase transitions in the XY chain and the XXZ model. The quantum correlated coherence has been introduced by Tan and Jeong [Phys. Rev. Lett. 121, 220401 (2018)]. We utilize the quantum correlated coherence to investigate the quantum critical systems. We also demonstrate the Hellinger distance which shows the quantum critical behaviors. The numerical results are presented and analyzed in details.