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We show that the new technique of terahertz 2D coherent spectroscopy iscapable of giving qualitatively new information about fractionalized spinsystems. For the prototypical example of the transverse field Ising chain, wedemonstrate theoretically that, despite the broad continuum of excitations inlinear response, the 2D spectrum contains sharp features that are a coherentsignature of a `spinon echo', which gives previously inaccessible informationsuch as the lifetime of the two-spinon excited state. The effects of disorderand finite lifetime, which are practically indistinguishable in the linearoptical or neutron response, manifest in dramatically different fashion in the2D spectra. Our results may be directly applicable to model quasi-1D transversefield Ising chain systems such as CoNb$_2$O$_6$, but the concept can be appliedto fractionalized spin systems in general.

Resolving continua of fractional excitations by spinon echo in THz 2D coherent spectroscopy