Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Localization of disordered bosons and magnets in random fields

Journal Article · · Annals of Physics (New York)
 [1];  [2]
  1. International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste (Italy)
  2. The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)
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, ξ{sup −1}(ω)=ξ{sup −1}(0)+A|ω|{sup α}, with α 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. -- Highlights: •Study of localization properties of disordered bosons and spins in random fields. •Comparison between XY magnets (hard-core bosons) and Ising magnets. •Analysis of the nature of the magnetic transition in strong quenched disorder. •Ising magnets: activated scaling, no closing mobility gap at the transition. •Ising order emerges on sparser (fractal) support than XY order.
OSTI ID:
22224214
Journal Information:
Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 337; ISSN APNYA6; ISSN 0003-4916
Country of Publication:
United States
Language:
English

Similar Records

Real-space renormalization-group study of random-superconductor models
Journal Article · Sat Jun 01 00:00:00 EDT 1991 · Physical Review, B: Condensed Matter; (USA) · OSTI ID:5570551

Robustness of vortex-bound Majorana zero modes against correlated disorder
Journal Article · Sun Jul 11 20:00:00 EDT 2021 · Physical Review. B · OSTI ID:1817573

Supersolid Phase of Hard-Core Bosons on a Triangular Lattice
Journal Article · Thu Dec 01 23:00:00 EST 2005 · Physical Review Letters · OSTI ID:20699661