Localization of disordered bosons and magnets in random fields

Abstract

We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω= 0, ${\xi }^{-1}(\omega )={\xi }^{-1}(0)+A|\omega {|}^{\alpha }$, with $\alpha$ vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω= 0. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω= 0, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed.

27 pages, 8 figures

References in corpus (19)

• Anderson Transitions
• The large deviation approach to statistical mechanics
• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Bose-Einstein Condensation in Magnetic Insulators
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Ergodicity breaking in a model showing many-body localization
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to Bose-Einstein Condensate
• Evidence for a Superglass State in Solid 4He
• Phase transition of one dimensional bosons with strong disorder
• Bogoliubov Excitations of Disordered Bose-Einstein Condensates
• Phase transition of interacting disordered bosons in one dimension
• Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees
• Disordered bosons in one dimension: from weak to strong randomness criticality
• Bogoliubov theory on the disordered lattice
• Compensation driven superconductor-insulator transition
• Superconductor-insulator transition in Coulomb disorder

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• Localized Spin-Wave Modes and Microwave Absorption in Random-Anisotropy Ferromagnets
• Scaling of Static and Dynamical Properties of Random Anisotropy Magnets
• Static and Microwave Properties of Amorphous Magnets Near Saturation
• Fluctuation driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization