News & Events

Seminar by Dr. Satyaki Kar

Tuesday, January 17, 2017 - 09:30
SPS Seminar Room, NISER
Dr. Satyaki Kar
Indian Association for Cultivation of Science
Dr. V. Ravi Chandra

We study the long time dynamics in closed quantum systems periodically driven via time dependent pa-rameters with two frequencies ω1 and ω2 = rω1. Tuning of the ratio r there can unleash plenty of dynamicalphenomena to occur. Our study includes integrable models like Ising and XY models in d = 1 and Kitaev modelin d = 1 and 2 and can also be extended to Dirac fermions in graphene. We witness the wave-function over-lap or dynamic freezing to occur within some small/ intermediate frequency regimes in the (ω1, r) plane (withr 6= 0) when the ground state is evolved through single cycle of driving. However, evolved states soon becomesteady with long driving and the freezing scenario gets rarer. We extend the formalism of adiabatic-impulse ap-proximation for many cycle driving within our two-rate protocol and show the near-exact comparisons at smallfrequencies. An extension of the rotating wave approximation is also developed to gather an analytical frame-work of the dynamics at high frequencies. Finally we compute the entanglement entropy in the stroboscopicallyevolved states within the gapped phases of the system and observe how it gets tuned with the ratio r in ourprotocol. The minimally entangled states are found to fall within the regime of dynamical freezing. In general,the results indicate that the entanglement entropy in our driven short-ranged integrable systems follow genuinenon-area law of scaling and show a convergence (with a r dependent pace).

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