Localization for random block operators related to the XY spin chain

Abstract

We study a class of random block operators which appear as effective one-particle Hamiltonians for the anisotropic XY quantum spin chain in an exterior magnetic field given by an array of i.i.d. random variables. For arbitrary non-trivial single-site distribution of the magnetic field, we prove dynamical localization of these operators at non-zero energy.

27 pages, to appear in Annales Poincaré, new Theorem 7.2 added in final version

References in corpus (7)

• Localization of interacting fermions at high temperature
• The many-body localization phase transition
• Many body localization in Heisenberg XXZ magnet in a random field
• Dynamical Localization in Disordered Quantum Spin Systems
• Disorder-assisted error correction in Majorana chains
• Localization for random block operators
• Random Block Operators

Cited by in corpus (13)

• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
• Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
• A uniform area law for the entanglement of eigenstates in the disordered XY chain
• On transport properties of isotropic quasiperiodic $XY$ spin chains
• Entanglement Dynamics of Disordered Quantum XY Chains
• Large deviations for products of random two dimensional matrices
• Decay of Determinantal and Pfaffian Correlation Functionals in One-dimensional Lattices
• Slow propagation in some disordered quantum spin chains
• Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities
• Pseudo-gaps for random hopping models
• Bounded light cone and robust topological order out of equilibrium
• Structural constraints on mobility edges in one-dimensional quasiperiodic systems