Various series expansions for a Heisenberg antiferromagnet model for SrCu$_2$(BO$_3$)$_2$

TL;DR

This paper applies various series expansion methods to study the phase transition and parameter estimation of a Heisenberg antiferromagnet model relevant to SrCu$_2$(BO$_3$)$_2$, confirming a first-order quantum phase transition at a specific interaction ratio.

Contribution

It introduces multiple series expansion techniques at zero and finite temperature to analyze the model, providing more precise estimates of critical parameters and phase transition point.

Findings

Confirmed first-order quantum phase transition at x=0.691(6)

Located the transition point between gapped and gapless phases

Provided improved estimates of model parameters from susceptibility data

Abstract

We use a variety of series expansion methods at both zero and finite temperature to study an antiferromagnetic Heisenberg spin model proposed recently by Miyahara and Ueda for the quasi two-dimensional material SrCu$_2$(BO$_3$)$_2$. We confirm that this model exhibits a first-order quantum phase transition at T=0 between a gapped dimer phase and a gapless N\'eel phase when the ratio $x=J'/J$ of nearest and next-nearest neighbour interactions is varied, and locate the transition at $x_c=0.691(6)$. Using longer series we are able to give more accurate estimates of the model parameters by fitting to the high temperature susceptibility data.