Dimensional reduction at a quantum critical point

Abstract

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 (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-(1/2) 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.

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

“…The reduction of the two-dimensional kagome spin ice into one-dimensional 'stringy' reversed regions is a consequence of the frustrating effect of the dipolar interaction in kagome ice. Quite generally, this effect is known as 'dimensional reduction due to frustration' [15,16]. It is clear that disorder plays a crucial role for the observation of monopole defects.…”

“…The formation of Dirac strings occurs in the form of one-dimensional avalanches in a two-dimensional system. Being in stark contrast to the standard nucleation in two-dimensional films [14], the observed behaviour provides a novel example of dimensional reduction [15,16] due to the frustrating effect of the dipolar interactions together with non-collinear anisotropies. After a brief discussion of the experimental results [17], we shall show that they are in excellent agreement with Monte Carlo (MC) simulations of point dipoles on a kagome lattice.…”

Low-temperature heat transport of spin-gapped quantum magnets

“…For some particular spin-gapped quantum magnets, the XY-type AFM state induced by the external magnetic field that close the spin gap can be described as a magnon BEC state [21][22][23][24][25][26][27][28][29]. It can result in a QPT from the low-field disordered phase to the high-field long-range ordered state.…”

Phase separation versus supersolid behavior in frustrated antiferromagnets

“…1) and, remarkably, exotic quantum criticality has been detected in the spindimer compound BaCuSi 2 O 6 . [4][5][6][7] The presence of magnetic frustration further adds to the rich phenomenology of these systems by enhancing repulsive interactions between triplons, something that may eventually stabilize incompressible phases that break the lattice's translational symmetry. 2,8 Such crystalline phases are for instance realized in the Shastry-Sutherland material SrCu 2 (BO 3 ) 2 , 9,10 where they are signaled by a series of magnetization plateaux at unconventional fillings stabilized by complex triplon interactions.…”