Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains

It has long been known that the low-energy dynamics of spin systems are well-described by classical linear spin-wave theory. This is particularly true in the case of systems with a large spin moment, where one can expand in powers of 1/S. For large-spin antiferromagnets, linear spin wave theory predicts dispersive magnon modes which are gapped in the presence of anisotropy. Such spectra are found time and again in the literature, but can the quantum nature of spin give rise to exotic excitations that are not well described by linear spin-wave theory?
Using a path integral approach [1], we show that the movement of domain walls in an anisotropic large-spin antiferromagnetic chain can be described by solitons. In the presence of weak coupling to other chains, the frustration induced by this soliton propagation leads to a nonlinear confinement potential that can support bound states [2]. We will then show possible experimental evidence for these soliton bound states [3], demonstrate strong agreement with our theoretical model and offer insights into where one might expect to find such a phenomenon.

[1] F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)
[2] H. Lane et al, Phys. Rev. B 102, 024437 (2020)
[3] C. Stock et al, Phys. Rev. Lett. 117, 017201 (2016)