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arXiv · 1501.02109

Decay of transverse correlations in quantum Heisenberg models

Jakob E. Björnberg·Daniel Ueltschi
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Abstract

We study a class of quantum spin systems that includes the $S=\tfrac12$ 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.

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Jakob E. Björnberg, Daniel Ueltschi. 2015-01-09. Decay of transverse correlations in quantum Heisenberg models. https://doi.org/10.1063/1.4918675

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