On the confinement of spinons in the $CP^{M-1}$ model

TL;DR

This paper investigates how spinons in the $CP^{M-1}$ model become confined at finite temperature, showing that interactions turn the susceptibility's branch cut into simple poles, indicating confinement.

Contribution

It demonstrates that finite-temperature effects and $1/M$ corrections cause the confinement of spinons, transforming the susceptibility's analytic structure from a branch cut to simple poles.

Findings

Divergent $1/M$ corrections near the branch cut at finite temperature.

Full static susceptibility exhibits simple poles, indicating confinement.

Comparison with $O(N)$ sigma-model expansion.

Abstract

We use the $1/M$ expansion for the $CP^{M-1}$ model to study the long-distance behaviour of the staggered spin susceptibility in the commensurate, two-dimensional quantum antiferromagnet at finite temperature. At $M=\infty$ 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.