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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
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 | ||||||||
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| Subjects: | Q Science > QC Physics | ||||||||
| Divisions: | Faculty of Science > Mathematics Faculty of Science > Physics |
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| 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: |
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| Date of first compliant deposit: | 27 June 2016 | ||||||||
| 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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