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 in terms of group velocities of their effective Hamiltonians: $\mathfrak{v}\ge {\mathrm{ess}\sup }_{[0,1]}\frac{2}{\pi }\frac{dE}{dN},$ where $E$ is considered as a function of the integrated density of states.

13 pages

References in corpus (6)

• Dynamical Localization in Disordered Quantum Spin Systems
• Motion in Periodic Potentials
• Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
• Localization for random block operators related to the XY spin chain
• Many-Body Localization: Concepts and Simple Models
• A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies

Cited by in corpus (10)

• Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
• Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems
• On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field
• Maximal Speed of Propagation in Open Quantum Systems
• On Lieb-Robinson bounds for a class of continuum fermions
• On the relation between strong ballistic transport and exponential dynamical localization
• Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
• Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators
• Ballistic Transport for Periodic Jacobi Operators on ${\mathbb{Z}}^d$
• Stochastic process emerged from lattice fermion systems by repeated measurements and large-time limit