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arXiv:cond-mat/9508145 · Journal of Applied Physics

Order-parameter fluctuations in the frustrated Heisenberg model on the square lattice

Shu Zhang, Gerhard H. Muller

Published Apr 15, 1996• 0 citations
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Abstract

The T=0 dynamics of the two-dimensional s=1/2 Heisenberg model with competing nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions is explored via the recursion method, specifically the frequency-dependent fluctuations of the order parameters associated with some of the known or suspected ordering tendencies in this system, i.e., Néel, collinear, dimer, and chiral order. The results for the dynamic structure factors of the respective fluctuation operators show a strong indication of collinear order at J2/J1≳0.6 and a potential for dimer order at 0.5≲J2/J1≲0.6, whereas the chiral ordering tendency is observed to be considerably weaker.

DOI
10.1063/1.361906

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We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg J1{J}_{1}J1​-J2{J}_{2}J2​ model on an $L\ifmmode\times\else\texttimes\fi{}L$ square lattice with LLL === 8, 16, and 32. By treating tensor elements as variational parameters, we obtain the ground states for different J2/J1{J}_{2}/{J}_{1}J2​/J1​ values, and investigate staggered magnetizations, nearest-neighbor spin-spin correlations, and plaquette order parameters. In addition to the well-known N\'eel order and collinear order at low and high J2/J1{J}_{2}/{J}_{1}J2​/J1​, we observe a plaquettelike order at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.5$. A continuous transition between the N\'eel order and the plaquettelike order near ${J}_{2}^{{c}_{1}}\ensuremath{\approx}0.40{J}_{1}$ is observed. The collinear order emerges at ${J}_{2}^{{c}_{2}}\ensuremath{\approx}0.62{J}_{1}$ through a first-order phase transition.
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