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Periodic Driving of an Impurity in the Isotropic XY Chain

Livia Corsi, Giuseppe Genovese

Published Sep 24, 2016• 2 citations
OpenAlex

Abstract

We study the isotropic XY chain with a transverse magnetic field acting on a single site and analyse the long time behaviour of the time-dependent state of the system when a periodic perturbation drives the impurity. We find that for high frequencies the state approaches a periodic orbit synchronised with the forcing and provide the explicit rate of convergence to the asymptotics.

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We study the isotropic XY chain with a transverse magnetic field acting on a single site and analyse the long time behaviour of the time-dependent state of the system when a periodic perturbation drives the impurity. We find that for high frequencies the state approaches a periodic orbit synchronised with the forcing and provide the explicit rate of convergence to the asymptotics.
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.
Abstract 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.
Using a numerical approach we examine the dynamics of zzzzzz correlations for the spin-121\over221​ isotropic XY chain with random Lorentzian intersite coupling and transverse field at sites that depends linearly on the neighbouring couplings. We study in detail the wave vector- and frequency-dependent zzzzzz structure factor at different values of Hamiltonian parameters and temperature. We discuss the changes in the frequency profiles of the zzzzzz dynamic structure factor caused by the introduced correlated disorder.