Effect of perturbations on the kagome $S=1/2$ antiferromagnet at all temperatures

TL;DR

This study uses high temperature series expansions to analyze the thermodynamic properties of the kagome $S=1/2$ antiferromagnet across all temperatures, exploring effects of various perturbations and proposing experimental methods to determine zero-temperature susceptibility.

Contribution

It introduces an advanced entropy-based HTSE method with unprecedented order and applies it to study perturbations in the kagome antiferromagnet across all temperatures.

Findings

Identifies different low-temperature behaviors for the specific heat.

Analyzes effects of anisotropy, Dzyaloshinskii-Moriya interactions, and vacancies.

Proposes experimental approach to measure zero-temperature susceptibility.

Abstract

The ground state of the $S=1/2$ kagome Heisenberg antiferromagnet is now recognized as a spin liquid, but its precise nature remains unsettled, even if more and more clues point towards a gapless spin liquid. We use high temperature series expansions (HTSE) to extrapolate the specific heat $c_V(T)$ and the magnetic susceptibility $\chi(T)$ over the full temperature range, using an improved entropy method with a self-determination of the ground state energy per site $e_0$. Optimized algorithms give the HTSE coefficients up to unprecedented orders (20 in $1/T$) and as exact functions of the magnetic field. Three extrapolations are presented for different low-$T$ behaviors of $c_V$: exponential (for a gapped system), linear or quadratic (for two different types of gapless spin liquids). We study the effects of various perturbations to the Heisenberg Hamiltonian: Ising anisotropy, Dzyaloshinskii-Moriya interactions, second and third neighbor interactions, and randomly distributed magnetic vacancies. We propose an experimental determination of $\chi(T=0)$, which could be non zero, from $c_V$ measurements under different magnetic fields.