Non-magnetic impurities as a quantum microscope of finite size effects in spin chains

Overview & Synopsis

Finite-size effects are ubiquitous in quantum matter, yet typically invisible in the thermodynamic limit; when system size is restricted, boundaries and confinement reveal modified spectra, correlations, and emergent phenomena. With growing access to well-controlled few-spin systems, these effects are now directly observable and offer a route to probing universal physics and enabling quantum information applications. Here, we study finite-size physics in the quasi-one-dimensional Ising-like quantum antiferromagnet Ba(Co$_{1-x}$Mg$_x$)$_2$V$_2$O$_8$ with $x = 2\%$ and $x = 5\%$, where non-magnetic Mg$^{2+}$ ions fragment the Co$^{2+}$ spin chains into finite segments. Combining inelastic neutron scattering and numerical calculations, we identify distinct regimes with fundamentally different low-energy quantum excitations: spinons confined to chain boundaries, and a cluster mode in shorter chains corresponding to a collective reversal of the Néel-ordered segment without classical analogue. Our results demonstrate how chemical substitution acts as a quantum microscope providing direct access to boundary-shaped excitations in strongly correlated spin systems.