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Entangled quantum state of magnetic dipoles

Abstract

Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors1 and certain rare-earth intermetallics2, the 1/T law is replaced by a power law T-α with α < 1. Here we show that a much simpler material system—namely, the insulating magnetic salt LiHoxY1-xF4—can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data3, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects—entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom—becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.

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Figure 1: Magnetic susceptibility χ versus temperature T of the diluted, dipolar-coupled Ising magnet, LiHo0.045Y0.955F4.
Figure 2: Comparison of the temperature-dependent experimental electronic specific heat C(T) for LiHo0.045Y0.955F4 with different simulation techniques.
Figure 3: Diagram detailing the difference between the classical and the quantum decimation schemes.
Figure 4: The change in susceptibility as the quantum entanglement is tuned by varying the ratio of the transverse and longitudinal magnetic g-factors, g/g||.

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Acknowledgements

We thank R. Parthasarathy for discussions. The work at the University of Chicago was supported by the MRSEC Program of the National Science Foundation, that in the University of Wisconsin by the Petroleum Research Fund and the National Science Foundation, and that in University College London by a Wolfson–Royal Society Research Merit Award and the Basic Technologies programme of the UK Research Councils.

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Correspondence to T. F. Rosenbaum.

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Ghosh, S., Rosenbaum, T., Aeppli, G. et al. Entangled quantum state of magnetic dipoles. Nature 425, 48–51 (2003). https://doi.org/10.1038/nature01888

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