Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems

Abstract

We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamics are ballistic in a rather strong sense; namely, the (normalized) Heisenberg evolution of the position operator converges strongly to a self-adjoint operator that is injective on the space of absolutely summable sequences. In particular, this means that all transport exponents corresponding to well-localized initial states are equal to one. Our result may be applied to a class of quantum many-body problems. Specifically, we establish a lower bound on the Lieb--Robinson velocity for an isotropic XY spin chain on the integers with limit-periodic couplings.

20 pages

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Cited by in corpus (8)

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• Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
• Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk
• Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks
• Ballistic Transport for Periodic Jacobi Operators on ${\mathbb{Z}}^d$
• Thin Spectra and Singular Continuous Spectral Measures for Limit-Periodic Jacobi Matrices