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, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>γ</a:mi><a:mo>=</a:mo><a:msub><a:mi>J</a:mi><a:mi>y</a:mi></a:msub><a:mo>/</a:mo><a:msub><a:mi>J</a:mi><a:mi>x</a:mi></a:msub></a:mrow></a:math>. 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.