Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model

TL;DR

This study uses Schwinger-boson mean-field theory to show that in the kagome antiferromagnetic Heisenberg model, the spin gap quickly fills with temperature due to spinon deconfinement, affecting spectral properties before spinon density increases.

Contribution

It reveals how the spin gap in a $ ext{Z}_2$ spin liquid rapidly fills with temperature, highlighting the role of spinon deconfinement in spectral changes.

Findings

Spectral gap fills rapidly with temperature before spinon density increases.

Low-energy spectral weight develops at T ≈ Δ/3 due to deconfinement.

Schwinger-boson mean-field approach breaks down at high temperatures.

Abstract

Using Schwinger-boson mean-field theory, we calculate the dynamic spin structure factor at low temperatures $0<T\ll J$ for the spin-$1/2$ antiferromagnetic Heisenberg kagome model, within the gapped $\mathbb{Z}_2$ spin liquid phase Ansatz. We find that the spectral gap rapidly fills with temperature, with robust low-energy spectral weight developing by a temperature of $\Delta/3$, where the spin gap is $2\Delta$ (i.e., $\Delta$ is the spinon gap), before any appreciable rise in spinon density or change in zero-temperature mean-field parameters. This is due to deconfinement of spinons which leads to terms suppressed only by $\exp(-\Delta/T)$. At still higher temperatures, the spinon density increases rapidly leading to a breakdown of the Schwinger-boson mean-field approach. We suggest that if the impurity-free spectral functions can be obtained through neutron scattering experiments on kagome herbertsmithites, temperature dependence of the subgap weight can provide distinct signatures of a $\mathbb{Z}_2$ quantum spin liquid.