  Competition between electronic ground states near a quantum critical point
(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 systems. New electronic phases of matter have been
predicted to occur in the vicinity of a QCP by two-dimensional theories, 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.
Here we show evidence that the Bose-Einstein condensate of spin triplets in the
three-dimensional Mott insulator BaCuSi2O6 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-1/2 Cu2+ pairs (spin dimers) to become decoupled
at the QCP, giving rise to a two-dimensional QCP characterized by 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.
