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Dimensional reduction at a quantum critical point


Competition between electronic ground states near a quantum critical point1,2 (QCP)—the location of a zero-temperature phase transition driven solely by quantum-mechanical fluctuations—is expected to lead to unconventional behaviour in low-dimensional systems3. New electronic phases of matter have been predicted to occur in the vicinity of a QCP by two-dimensional theories3,4,5,6,7,8, and explanations based on these ideas have been proposed for significant unsolved problems in condensed-matter physics, such as non-Fermi-liquid behaviour and high-temperature superconductivity. But the real materials to which these ideas have been applied are usually rendered three-dimensional by a finite electronic coupling between their component layers; a two-dimensional QCP has not been experimentally observed in any bulk three-dimensional system, and mechanisms for dimensional reduction have remained the subject of theoretical conjecture9,10,11. Here we show evidence that the Bose–Einstein condensate of spin triplets in the three-dimensional Mott insulator BaCuSi2O6 (refs 12–16) provides an experimentally verifiable example of dimensional reduction at a QCP. The interplay of correlations on a geometrically frustrated lattice causes the individual two-dimensional layers of spin-½ Cu2+ pairs (spin dimers) to become decoupled at the QCP, giving rise to a two-dimensional QCP characterized by linear power law scaling distinctly different from that of its three-dimensional counterpart. Thus the very notion of dimensionality can be said to acquire an ‘emergent’ nature: although the individual particles move on a three-dimensional lattice, their collective behaviour occurs in lower-dimensional space.

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Figure 1: Experimentally obtained phase boundary of BaCuSi2O6.
Figure 2: Crossover from 3D to 2D BEC critical exponent.
Figure 3: 2D BEC power law behaviour.
Figure 4: Inter-layer decoupling at the QCP.


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N.H., C.D.B., M.J. and P.A.S. acknowledge Laboratory Directed Research and Development (LDRD) support at LANL. S.E.S and I.R.F. acknowledge National Science Foundation (NSF) support. Experiments performed at the NHMFL, Tallahassee, were supported by the NSF, the State of Florida, and the Department of Energy. We thank T. P. Murphy, E. C. Palm, P. Tanedo and P. B. Brooks for experimental assistance, and acknowledge discussions with A. G. Green, E.-A. Kim, S. A. Kivelson, D. I. Santiago and J. Schmalian. I.R.F. acknowledges support from the Alfred P. Sloan Foundation and S.E.S. from the Mustard Seed Foundation.

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Sebastian, S., Harrison, N., Batista, C. et al. Dimensional reduction at a quantum critical point. Nature 441, 617–620 (2006).

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