Geometric Frustration and Dimensional Reduction at a Quantum Critical Point

We show that the spatial dimensionality of the quantum critical point associated with Bose--Einstein condensation at T=0 is reduced when the underlying lattice comprises a set of layers coupled by a frustrating interaction. Our theoretical predictions for the critical temperature as a function of the chemical potential correspond very well with recent measurements in BaCuSi$_{2}$O$_{6}$ [S. E. Sebastian \textit{et al}, Nature \textbf{411}, 617 (2006)].