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arXiv:0901.3141 · Physical Review B

Phase diagram of the frustrated spatially-anisotropic S=1 antiferromagnet on a square lattice

Hong‐Chen Jiang, Frank Krüger, Joel E. Moore, D. N. Sheng, Jan Zaanen, Zheng-Yu Weng

Published May 7, 2009• 53 citations
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Abstract

We study the $S=1$ square lattice Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor couplings ${J}_{1x}$ and ${J}_{1y}$ frustrated by a next-nearest-neighbor coupling ${J}_{2}$ numerically using the density-matrix renormalization-group (DMRG) method and analytically employing the Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the N\'eel-ordered state above the classically stable region. Whereas SBMFT suggests a fluctuation-induced first-order transition between the N\'eel state and a stripe antiferromagnet for $1/3\ensuremath{\le}{J}_{1x}/{J}_{1y}\ensuremath{\le}1$ and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum-disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for $S=1$ quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.

DOI
10.1103/physrevb.79.174409

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We study the effect of spin anisotropies on a frustrated quantum antiferromagnet using the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}^{XXZ}$ model on the square lattice. The T=0T=0T=0 and finite-TTT phase diagrams of this model are obtained utilizing spin-wave theory, exact diagonalization, and quantum Monte Carlo calculations. We find that anisotropic frustration tends to stabilize XYXYXY- and Ising-like ordered phases, while the disordered spin-liquid phase is restricted to a small region of the phase diagram. The ordered phases are separated by first-order transitions and exhibit a nontrivial reentrance phenomenon.
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