Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons

Abstract

Based on the mapping between $s=1/2$ spin operators and hard-core bosons, we extend the cluster perturbation theory to spin systems and study the whole excitation spectrum of the antiferromagnetic $J_1$-$J_2$ Heisenberg model on the square lattice. In the Néel phase for $J_2\lesssim 0.4J_1$, in addition to the dominant magnon excitation, there is an obvious continuum close to $(\ddot{I}€,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon excitations. In the stripe phase for $J_2\gtrsim 0.6J_1$, we find similar high-energy two-spinon continuums at $(\ddot{I}€/2,\ddot{I}€/2)$ and $(\ddot{I}€/2,\ddot{I}€)$, respectively. The intermediate phase is characterized by a spectrum with completely deconfined broad continuum, which is attributed to a $Z_2$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis.

7 pages, 6 figures