  The transition between the N\'{e}el antiferromagnet and the valence-bond
solid state in two dimensions has become a paradigmatic example of deconfined
quantum criticality, a non-Landau transition characterized by fractionalized
excitations (spinons). We consider an extension of this scenario whereby the
deconfined spinons are subject to a magnetic field. The primary purpose is to
identify the exotic scenario of a Bose-Einstein condensate of spinons. We
employ quantum Monte Carlo simulations of the \mbox{$J$-$Q$} model with a
magnetic field and perform a quantum field theoretic analysis of the magnetic
field and temperature dependence of thermodynamic quantities. The combined
analysis provides compelling evidence for the Bose-Einstein condensation of
spinons and also demonstrates an extended temperature regime in which the
system is best described as a gas of spinons interacting with an emergent gauge
field.
