Communications in Mathematical Physics

, Volume 134, Issue 2, pp 237–272

Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts III and IV

  • Claudio Albanese
Article

DOI: 10.1007/BF02097702

Cite this article as:
Albanese, C. Commun.Math. Phys. (1990) 134: 237. doi:10.1007/BF02097702

Abstract

This is the continuation of a series of articles concerning a class of quantum spin systems with Hamiltonian operators of the form
$$H_\lambda = \sum\limits_{x \in \Lambda } {s_x + } \sum\limits_{yo \subset \Lambda } {\lambda ^{\left| {yo} \right|_c - 1} } t_{yo} $$
where Λ is a graph, λ is a small parameter andsx has a gap≥1 for all x ε Λ\I In the singular setI ⊂ Λ, the gap ofsx can be arbitrarily small. Part III is devoted to the proof of a preliminary result, while in Part IV we consider the case in whichI is a subset of finite density of Λ. This completes the first iteration step of the deterministic part of the proof of localization in the ground state of the random field quantumXY model.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Claudio Albanese
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA