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Quantum magnetism and criticality

Nature Physics volume 4, pages 173–185 (2008)Cite this article

Abstract

Magnetic insulators have proved to be fertile ground for studying new types of quantum many-body state, and I survey recent experimental and theoretical examples. The insights and methods also transfer to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle- or wave-like interpretation, and control a significant portion of the finite-temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black holes.

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Figure 1: Néel states.
Figure 2: The coupled-dimer antiferromagnet.
Figure 3: Valence-bond solid states.
Figure 4: Caricature of a spin-liquid state.
Figure 5: Histogram of the VBS order parameter.

© 2007 APS

Figure 6: Bosons with repulsive interactions on a square lattice at filling f=1.
Figure 7: Bosons with repulsive interactions on a square lattice at filling f=1/2.
Figure 8: Structures of possible insulating states on the square lattice for paired electrons at a hole density of x=1/8 (f=1/16).

© 2005 APS

Figure 9: Phase diagram of the superfluid–insulator transition in two dimensions.
Figure 10: Superfluid–insulator transition applied to the cuprate superconductors.

© 2007 AAAS

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Acknowledgements

I thank S. Bais, S. Hartnoll, R. Kaul, R. Melko, M. Metlitski, M. Müller and A. Sandvik for valuable comments. This work was supported by NSF Grant No. DMR-0537077.

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    Subir Sachdev

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Sachdev, S. Quantum magnetism and criticality. Nature Phys 4, 173–185 (2008). https://doi.org/10.1038/nphys894

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