Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange

TL;DR

This study maps the phase diagram of a 3D spin-1/2 Heisenberg antiferromagnet with competing interactions, identifying a first-order quantum transition and critical lines at finite temperatures using linked-cluster series expansions.

Contribution

It provides the first detailed phase diagram analysis of the BCC S=1/2 Heisenberg antiferromagnet with first and second neighbor exchanges at both zero and high temperatures.

Findings

First-order quantum phase transition at J2/J1 ≈ 0.705

Accurate estimates of the critical line for the AF1 phase

Identification of a bicritical point at J1/J2 ≈ 0.71 and T ≈ 0.34 J1

Abstract

We use linked-cluster series expansions, both at T=0 and high temperature, to analyse the phase structure of the spin-$\half$ Heisenberg antiferromagnet with competing first and second-neighbor interactions on the 3-dimensional body-centred-cubic lattice. At zero temperature we find a first-order quantum phase transition at $J_2/J_1 \simeq 0.705 \pm 0.005$ between AF$_1$ (Ne\'el) and AF$_2$ ordered phases. The high temperature series yield quite accurate estimates of the bounding critical line for the AF$_1$ phase, and an apparent critical line for the AF$_2$ phase, with a bicritical point at $J_1/J_2\simeq 0.71$, $kT/J_1\simeq 0.34$. The possibility that this latter transition is first-order cannot be excluded.