Spin-1/2 Heisenberg-Antiferromagnet on the Kagome Lattice: High Temperature Expansion and Exact Diagonalisation Studies

TL;DR

This study uses high temperature series and exact diagonalisation to analyze the thermodynamic properties and spin correlations of the spin-1/2 Heisenberg antiferromagnet on the Kagome lattice, revealing no magnetic order at low temperatures.

Contribution

It provides detailed high temperature series calculations and compares them with exact diagonalisation results, offering new insights into the low-temperature behavior of the Kagome lattice antiferromagnet.

Findings

Specific heat shows additional structure below the high temperature peak.

Structure factor at T=0.25 agrees with ground state of 36-site cluster.

Uniform susceptibility peaks at T≈1/6 and vanishes exponentially at lower T.

Abstract

For the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the Kagom\'e lattice we calculate the high temperature series for the specific heat and the structure factor. A comparison of the series with exact diagonalisation studies shows that the specific heat has further structure at lower temperature in addition to a high temperature peak at $T\approx 2/3$. At $T=0.25$ the structure factor agrees quite well with results for the ground state of a finite cluster with 36 sites. At this temperature the structure factor is less than two times its $T=\infty$ value and depends only weakly on the wavevector $\bf q$, indicating the absence of magnetic order and a correlation length of less than one lattice spacing. The uniform susceptibility has a maximum at $T\approx 1/6$ and vanishes exponentially for lower temperatures.