Deconfinement of spinons in frustrated spin systems: Spectral perspective

Abstract

The confinement and deconfinement of spinons in the square-lattice antiferromagnetic ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model are elaborated by exploring the evolution of the whole excitation spectra with ${J}_{2}$, based on the spin cluster perturbation theory. We find that deconfined spin-$1/2$ spinons beyond the conventional spin-1 magnons have already emerged partially even in the limit ${J}_{2}=0$ and develop with ${J}_{2}$, exhibiting as a continuum close to $(\ensuremath{\pi},0)$ in the Brillouin zone. In the region near ${J}_{2}=0.5{J}_{1}$, the entire spectrum is characterized by a broad continuum in which all magnons are deconfined into spinons, whose ground state is attributed to a ${Z}_{2}$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis. The spinon continua are also found in the stripe phase with ${J}_{2}>0.6{J}_{1}$. Our study provides spectroscopic evidences for the fractionalized excitations and quantum spin liquid and highlights the rising field to explore the exotic quantum phases from a perspective of excitation spectrum.