Residual entropy and spin gap in a one-dimensional analog of the pyrochlore antiferromagnet

TL;DR

This paper analyzes a one-dimensional model of coupled tetrahedra, revealing residual entropy and a spin gap, which provides insights into the properties of the pyrochlore antiferromagnet.

Contribution

It demonstrates that the low-energy spectrum of the 1D coupled tetrahedra model is a replica of the dimerized Heisenberg chain spectrum, proving residual entropy and a spin gap.

Findings

Residual ground-state entropy per spin is 2^{1/4}.

A singlet-triplet gap exists when inter-tetrahedral coupling is weaker than internal coupling.

Spectrum matches that of the dimerized Heisenberg chain.

Abstract

We show that the low-energy sector of the S=1/2, antiferromagnetic Heisenberg model on a one-dimensional lattice of coupled tetrahedra consists of 2^N replica of the spectrum of the dimerized Heisenberg chain, where N is the number of tetrahedra. This provides a proof of the following properties: i) there is a residual ground-state entropy per spin equal to 2^{1/4}; ii) there is a singlet-triplet gap as long as the coupling between the tetrahedra is smaller than the internal one. These properties are compared to available results on the pyrochlore lattice.