An outstanding question in frustrated quantum magnets in two dimensions is whether one can have excitations with fractional quantum numbers, i.e. spin-1/2 spinons. [See the discussion here].
It is possible to consider triplet excitations as a pair of confined (i.e. bound) spinons. This can be worked out in detail in one dimension where the spinons are domain walls. But it has also been claimed that the spinon description is unnecessary.
There is an interesting PRL by Ying Tang and Anders Sandvik, Confinement and Deconfinement of Spinons in Two Dimensions.
They consider the spinons that are present near the quantum phase transition from a Neel ordered state to a Valence Bond State (VBS). This transition is associated with "deconfined quantum critical point" which breaks a Landau paradigm that a transition between two states that break different symmetries should be first order.
They compute the intrinsic size and the confinement length of the spinons as the quantum critical point is approached. The picture that emerges of the spinons is that of Z_4 vortices, as originally proposed in a paper by Levin and Senthil [from which the figure below is taken].