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On Transport Properties of Isotropic Quasiperiodic XY Spin Chains

Abstract

We consider isotropic XY spin chains whose magnetic potentials are quasiperiodic and the effective one-particle Hamiltonians have absolutely continuous spectra. For a wide class of such XY spin chains, we obtain lower bounds on their Lieb–Robinson velocities \({\mathfrak{v}}\) in terms of group velocities of their effective Hamiltonians:

$$\mathfrak{v}{\geqslant} {\mathop {\rm ess sup}_{[0,1]}}\frac{2}{\pi}\frac{dE}{dN}.$$

where E is considered as a function of the integrated density of states.

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Correspondence to Ilya Kachkovskiy.

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Communicated by H. Spohn

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Kachkovskiy, I. On Transport Properties of Isotropic Quasiperiodic XY Spin Chains. Commun. Math. Phys. 345, 659–673 (2016). https://doi.org/10.1007/s00220-015-2474-x

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Keywords

  • Lyapunov Exponent
  • Rotation Number
  • Ballistic Transport
  • Quantum Spin System
  • Singular Continuous Spectrum