$J_1-J_2$ Quantum Heisenberg Antiferromagnet: Improved Spin-Wave Theories Versus Exact-Diagonalization Data

TL;DR

This paper compares improved spin-wave theories with exact-diagonalization data for the $J_1-J_2$ quantum antiferromagnet, revealing that traditional theories overestimate quantum fluctuations and that the Néel phase persists up to higher frustration levels than previously thought.

Contribution

It introduces an enhanced spin-wave approach that better aligns with exact data, refining the understanding of phase stability in the $J_1-J_2$ model.

Findings

Spin-wave theories overestimate quantum fluctuation effects.

Néel phase remains stable up to $J_2/J_1=0.49$, higher than earlier estimates.

Marshall-Peierls rule persists for $J_2/J_1<0.323$ in the frustrated regime.

Abstract

We reconsider the results cocerning the extreme-quantum $S=1/2$ square-lattice Heisenberg antiferromagnet with frustrating diagonal couplings ($J_1-J_2$ model) drawn from a comparison with exact-diagonalization data. A combined approach using also some intrinsic features of the self-consistent spin-wave theory leads to the conclusion that the theory strongly overestimates the stabilizing role of quantum flutcuations in respect to the N\'{e}el phase in the extreme-quantum case $S=1/2$. On the other hand, the analysis implies that the N\'{e}el phase remains stable at least up to the limit $J_{2}/J_{1} = 0.49$ which is pretty larger than some previous estimates. In addition, it is argued that the spin-wave ansatz predicts the existence of a finite range ($J_{2}/J_{1}<0.323$ in the linear spin-wave theory) where the Marshall-Peierls sigh rule survives the frustrations.