Confinement of spinons in the ${\mathrm{CP}}^{\mathit{M}\mathrm{-}1}$ model

We use the 1/M expansion for the ${\mathrm{CP}}^{\mathit{M}\mathrm{-}1}$ model to study the long-distance behavior of the staggered spin susceptibility in the commensurate, two-dimensional quantum antiferromagnet at finite temperature. At M=∞ this model possesses deconfined spin-1/2 bosonic spinons (Schwinger bosons), and the susceptibility has a branch cut along the imaginary k axis. We show that in all three scaling regimes at finite T, the interaction between spinons and gauge-field fluctuations leads to divergent 1/M corrections near the branch cut. We identify the most divergent corrections to the susceptibility at each order in 1/M and explicitly show that the full static staggered susceptibility has a number of simple poles rather than a branch cut. We compare our results with the 1/N expansion for the O(N) sigma model.