Abstract
Easy-plane quantum magnets are strikingly similar to superconductors, allowing for spin supercurrent and an effective superconducting phase stemming from their U(1) rotation symmetry around the z-axis. We uncover a generalized fractional Josephson effect with a periodicity that increases linearly with system size in one-dimensional spin-1/2 chains at selected anisotropies and phase-fixing boundary fields. The effect combines arbitrary integer periodicities in a single system, exceeding the 4π and 8π periodicity of superconducting Josephson effects of Majorana zero modes and other exotic quasiparticles. We reveal a universal energy-phase relation and connect the effect to the recently discovered phantom helices.