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

N. B. Ivanov·J. Richter
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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 Néel phase in the extreme-quantum case $S=1/2$. On the other hand, the analysis implies that the Néel 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.

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N. B. Ivanov, J. Richter. 1994-07-08. $J_1-J_2$ Quantum Heisenberg Antiferromagnet: Improved Spin-Wave Theories Versus Exact-Diagonalization Data. https://doi.org/10.1088/0953-8984%2F6%2F20%2F018

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