Björnberg, Jakob E. and Ueltschi, Daniel (2015) Decay of transverse correlations in quantum Heisenberg models. Journal of Mathematical Physics, 56 (4). pp. 1-9. 043303. doi:10.1063/1.4918675

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Abstract

We study a class of quantum spin systems that includes 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-representation of the correlation functions, on stochastic domination, and on first-passage percolation.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Heisenberg uncertainty principle
Journal or Publication Title:	Journal of Mathematical Physics
Publisher:	American Institute of Physics
ISSN:	0022-2488
Official Date:	20 April 2015
Dates:	Date Event 20 April 2015 Available 8 April 2015 Accepted 19 January 2015 Submitted
Volume:	56
Number:	4
Number of Pages:	9
Page Range:	pp. 1-9
Article Number:	043303
DOI:	10.1063/1.4918675
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Knut and Alice Wallenberg Foundation, Leverhulme Trust (LT)
Related URLs:	Publisher

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