Theory of the Field-Induced BEC in the Frustrated Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>Dimer Compound<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>BaCuSi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="bold">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

Building on recent neutron and NMR experiments, we investigate the field-induced exotic criticality observed in the frustrated compound ${\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}$ using a frustrated model with two types of bilayers. A semiclassical treatment of the effective hard-core boson model shows that perfect interlayer frustration leads to a 2D-like critical exponent $\ensuremath{\phi}=1$ without logarithmic corrections and to a 3D low temperature phase with different but nonvanishing triplet populations in both types of bilayers. These further suggest a simple phenomenology in terms of a field-dependent transverse coupling in the context of which we reproduce the entire field-temperature phase diagram with quantum Monte Carlo simulations.

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