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

## TL;DR

This paper demonstrates that terahertz 2D coherent spectroscopy can reveal sharp features and spinon echoes in fractionalized spin systems, providing new insights into their excitations and lifetimes beyond traditional methods.

## Contribution

The study introduces the concept of spinon echo detection via 2D spectroscopy, enabling access to information on fractional excitations and their lifetimes in spin systems.

## Key findings

- 2D spectra show sharp features despite broad linear response continua.
- Spinon echoes reveal the lifetime of two-spinon excited states.
- Disorder and finite lifetime effects are distinguishable in 2D spectra.

## Abstract

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