Confined and Deconfined Spinon Excitations in the Rectangular-lattice Quantum Antiferromagnet

Fractionalization remains one of the most fascinating manifestations of strong interactions in quantum many-body systems. In quantum magnetism, the existence of spinons-collective magnetic excitations that behave as quasiparticles with fractional quantum numbers-is proven in spin chains, but the criteria for their appearance in higher dimensions remain disputed. Motivated by experiments reporting the observation of spinons at high energies in the square-lattice Heisenberg antiferromagnet, we adopt the approach of extrapolating from where spinons are well defined. We study the dynamical properties of a Gutzwiller-projected wave function, the staggered-flux state, on a rectangular spin-1/2 Heisenberg lattice as a function of the spatial coupling ratio, gamma = Jy/Jx. By studying the spectrum and the spinon separation distribution we show how, as the system evolves from one-dimensional (1D) towards 2D, the spinons become progressively more confined over most of reciprocal space, but remain deconfined at specific wave vectors.