1. Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford, California 94305, USA
2. NHMFL, MS-E536, Los Alamos National Laboratory,
3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
4. National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
5. Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan

Correspondence to: S. E. Sebastian¹ Correspondence and requests for materials should be addressed to S.E.S. (Email: suchitra@stanfordalumni.org).

Abstract

Competition between electronic ground states near a quantum critical point^{1, 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 theories^{3, 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 conjecture^{9, 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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