The theoretical study of magnetism was initiated almost a century ago in the early years of quantum mechanics, and has continued to intrigue theorists ever since, playing a forefront role in the development of modern statistical physics. In recent decades, detailed experimental studies of magnetism in quantum materials have accelerated through better materials synthesis and various powerful spectroscopic probes, allowing for many abstract theoretical ideas of magnetism to meet experimental reality.  As a concrete illustration of this synergy, I will focus on our work* on the magnet CoNb2O6, a well known realization of one-dimensional Ising criticality.  I will show how through a combination of theoretical work and THz spectroscopy experiments we uncover rich domain wall dynamics, described by the celebrated Su-Schrieefer-Heeger model of polyacetylene. We are able to quantitatively explain the THz data by time-dependent matrix product state simulations of a simple spin model with bond-dependent exchange interactions induced by spin-orbit coupling, paving the way for a possible realization of exotic phase of matter called a "topological quantum spin liquid" in a wider class of materials.  As a by-product, I will show how our work on CoNb2O6 also provides the first direct physical observation of the Kramers-Wannier duality in a natural system. I will conclude the presentation with a short overview of how this project fits in my larger research program. 

*https://www.nature.com/articles/s41567-021-01208-0