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Criticality in correlated quantum matter

Nature Physics volume 1, pages 53–56 (2005)Cite this article

Abstract

At quantum critical points (QCPs) quantum fluctuations exist on all length scales, from microscopic to macroscopic, which, remarkably, can be observed at finite temperatures—the regime to which all experiments are necessarily confined. But how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? We answer these questions by examining exact solutions of models of systems with strong electronic correlations and find that QCPs can influence physical properties at surprisingly high temperatures. As a powerful illustration of quantum criticality, we predict that the zero-temperature superfluid density, ρs(0), and the transition temperature, Tc, of the high-temperature copper oxide superconductors are related by Tc∝ρs(0)y, where the exponent y is different at the two edges of the superconducting dome, signifying the presence of the respective QCPs. This relationship can be tested in high-quality crystals.

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Figure 1: The scaled free energy Φ(λ1=1, J /T) plotted as a function of 2J /T.
Figure 2: The critical lines of the Ising model in a transverse field with three-spin interaction.
Figure 3: The quantity Φ(λ1,λ2=1−λ1, J /T) is plotted as a function of 2J /T for different values of λ1 although maintaining criticality, that is, Δπ=0.
Figure 4: The scaled free energy density minus the ground-state energy density, (f −e 0)(ħ c) 2/T 3, of the quantum O(N)-nonlinear σ-model in the limit N →∞ (dotted line).

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Acknowledgements

We thank E. Fradkin, S. Sachdev, S. L. Sondhi, and A. P. Young for helpful comments on the manuscript and H. M. Rønnow and D. Bonn for the prepublication copies of refs 1824. This work was supported by the NSF under grant: DMR-0411931.

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  1. Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095-1547, USA

    Angela Kopp & Sudip Chakravarty

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  1. Angela Kopp
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Correspondence to Sudip Chakravarty.

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Kopp, A., Chakravarty, S. Criticality in correlated quantum matter. Nature Phys 1, 53–56 (2005). https://doi.org/10.1038/nphys105

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