Geometric Frustration and Dimensional Reduction at a Quantum Critical Point

1
Geometric Frustration and DimensionalReduction
at a Quantum Critical Point
Conventional dimensional crossover involves the
reduction in effective dimensionality away from a
critical point (CP) in highly anisotropic systems
-- sufficiently close to the CP, the full
dimensionality is restored. In contrast,
dimensional reduction can occur in geometrically
frustrated system as it approaches a Gaussian
quantum CP. This results from the nature of the
inter-layer coupling that vanishes right at the
QCP for a chemical potential tuned Bose-Einstein
condensation (BEC).
(a) A perfect AF order of the four spins in the
square plaquette precludes an effective coupling
between SB and ST. (b) A phase fluctuation
induceds and effective ferromagnetic coupling
between SB and ST For BaCuSi2O6 each site
represents a dimer.
This theory explains quantitatively the
dimensional reduction observed in the frustrated
magnet BaCuSi2O6. BaCuSi2O6 consists of S1/2
dimers on a body-centered tetragonal lattice --
the inter-layer interaction between the dimers is
frustrated. The field induced BEC-QCP belongs to
the (2D) BKT universality class. Excellent
agreement between theoretical predictions and
experimental results confirms the validity of the
theory.

C. D. Batista, et.al., Geometric Frustration and
Dimensional reduction at a Quantum Critical
point, Phys. Rev. Lett. 98, 257201 (2007).