Spinon deconfinement on domain walls

A valence-bond solid phase of a square-lattice antiferromagnet supports four dimer patterns (vacua) related by the Z4 lattice rotational symmetries. Such a system allows for stable domain walls between regions in different vacua. We here discuss a system in a wide-strip geometry, where boundary conditions enforce two parallel domain walls along the long direction. In this system a spin-1 excitation deconfines into two spin-1/2 spinons, even though such excitations are confined into conventional spin-1 "triplons" in the bulk because of the confining strings formed when spinons are separated. In the geometry we consider, the domain walls absorb the confining strings, leading to a finite energy of creating the spinons. We confirm this scenario by quantum Monte Carlo simulations of the J-Q spin model, showing that, by tuning the width of the strip (thedistance between the domain walls), we can control the mass of such deconfined spinon excitation.