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Title: Decay of transverse correlations in quantum Heisenberg models

We study a class of quantum spin systems that include the S=1/2 Heisenberg and XY-models and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random loop representations of the correlation functions, on stochastic domination and on first-passage percolation.
Authors:
 [1] ;  [2]
  1. Department of Mathematical Sciences, Chalmers and University of Gothenburg, 41296 Göteborg (Sweden)
  2. Department of Mathematics, University of Warwick, Coventry CV4 7AL (United Kingdom)
Publication Date:
OSTI Identifier:
22403137
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; HEISENBERG MODEL; MAGNETIC FIELDS; SPIN; STOCHASTIC PROCESSES