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

TL;DR

This paper investigates the excitation spectrum of the square-lattice J1-J2 Heisenberg model, revealing deconfined spinons and quantum spin liquid behavior across different phases using an extended cluster perturbation theory.

Contribution

It extends cluster perturbation theory to spin systems and provides detailed spectral analysis, highlighting deconfined spinons and quantum spin liquid states in the model.

Findings

Deconfined spin-1/2 spinons in the Néel phase near (π,0)

High-energy two-spinon continua in stripe phases at specific momenta

Evidence for a Z2 quantum spin liquid in the intermediate phase

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 N\'eel phase for $J_{2}\lesssim0.4J_{1}$, in addition to the dominant magnon excitation, there is an obvious continuum close to $(\pi,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon excitations. In the stripe phase for $J_{2}\gtrsim0.6J_{1}$, we find similar high-energy two-spinon continuums at $(\pi/2,\pi/2)$ and $(\pi/2,\pi)$, 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.