Controlled assembly and real-space connectivity of multiple spinon sources

Determine whether multiple spinon sources in the VBS phase of the square-lattice J–Q model near a deconfined quantum critical point can be assembled into controlled complexes and under what conditions their domain-wall connectivity can be resolved directly in real space.

Background

The paper studies confinement in the columnar valence-bond-solid phase near deconfined quantum criticality, where spinons appear as vortices of the VBS angle and are connected by VBS domain-wall strings. Because these strings are broad and weakly tensioned near the critical point, multiple pinned spinon sources could potentially form complexes with nontrivial connectivity, analogous to string-connected multi-charge states in gauge theories.

The authors address this question using pinned-spin defects and quantum Monte Carlo simulations, demonstrating dipole string breaking, connected four-spinon complexes, and extended domain-wall networks. The quoted passage nevertheless frames the general question of whether such complexes can be controlled and when their connectivity can be directly resolved as an unresolved issue; the subsequent results provide examples rather than a general characterization.