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Decay of transverse correlations in quantum Heisenberg models

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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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Official URL: http://dx.doi.org/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:
DateEvent
20 April 2015Available
8 April 2015Accepted
19 January 2015Submitted
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)
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