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Quantum criticality among entangled spin chains


An important challenge in magnetism is the unambiguous identification of a quantum spin liquid1,2, of potential importance for quantum computing. In such a material, the magnetic spins should be fluctuating in the quantum regime, instead of frozen in a classical long-range-ordered state. While this requirement dictates systems3,4 wherein classical order is suppressed by a frustrating lattice5, an ideal system would allow tuning of quantum fluctuations by an external parameter. Conventional three-dimensional antiferromagnets can be tuned through a quantum critical point—a region of highly fluctuating spins—by an applied magnetic field. Such systems suffer from a weak specific-heat peak at the quantum critical point, with little entropy available for quantum fluctuations6. Here we study a different type of antiferromagnet, comprised of weakly coupled antiferromagnetic spin-1/2 chains as realized in the molecular salt K2PbCu(NO2)6. Across the temperature–magnetic field boundary between three-dimensional order and the paramagnetic phase, the specific heat exhibits a large peak whose magnitude approaches a value suggestive of the spinon Sommerfeld coefficient of isolated quantum spin chains. These results demonstrate an alternative approach for producing quantum matter via a magnetic-field-induced shift of entropy from one-dimensional short-range order to a three-dimensional quantum critical point.

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Fig. 1: Comparison of the TH phase diagram for the quasi-1D system K2PbCu(NO2)6 with the behaviour of a generic 3D antiferromagnet.
Fig. 2: Magnetic properties of K2PbCu(NO2)6 showing quasi-1D behaviour and antiferromagnetic order.
Fig. 3: Specific heat divided by temperature, C(T,H)/T, versus magnetic field for K2PbCu(NO2)6.
Fig. 4: The temperature dependence of C/T(H) peaks suggests an explanation based on spinons in 1D.


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This work was supported by NSF-DMR 1534741 (A.P.R.), NSF-DMR1506119 (L.B.) and NSF-DMR 1534818 (T.S., L.D.). The research at Georgia Tech was supported by Oak Ridge Associated Universities through the Ralph E. Powe Junior Faculty Enhancement Award (M.M.). The research at Oak Ridge National Laboratory’s High Flux Isotope Reactor was sponsored by the US Department of Energy, Office of Basic Energy Sciences, Scientific User Facilities Division. The research at the National High Magnetic Field Laboratory was supported by the NSF Collaborative Agreement DMR 1157490 and the State of Florida. We thank G. Aeppli, M. E. Fisher, D. Reich and C. M. Varma for their helpful insights.

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A.P.R. designed the experiment, and with N.B. and J.T. collected and analysed specific-heat data. T.S. and L.D. grew crystals and analysed susceptibility data. X.B., A.A. and M.M. performed neutron scattering and magnetization measurements and analysed the data. L.B. provided theoretical interpretation of results.

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Correspondence to A. P. Ramirez.

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Supplementary note 1, Supplementary Figures 1&2, and Supplementary Reference 1

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Blanc, N., Trinh, J., Dong, L. et al. Quantum criticality among entangled spin chains. Nature Phys 14, 273–276 (2018).

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