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 S=1/2 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).