Communications in Theoretical Physics

Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

An-Chun Ji, Tian Guang-Shan

Published Jan 1, 2007• 3 citations

Abstract

In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferromagnetic Heisenberg model of S = 1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J ⊥ c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J ⊥ c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.

DOI: 10.1088/0253-6102/47/1/033

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Communications in Theoretical Physics

Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

An-Chun Ji, Tian Guang-Shan

Published Jan 1, 2007• 3 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/47/1/033

Related papers

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arXiv:cond-mat/0210394Physical review. B, Condensed matterAug 16, 200213 citations

In the present paper, we investigate the existence of the antiferromagnetic long-range order in a

S=1

spatially anisotropic antiferromagnetic Heisenberg model with a single-ion energy term. By applying the reflection-positivity method developed by Dyson, Lieb, and Simon [J. Stat. Phys. 53, 1019 (1988)], we are able to determine the parameter regions where either the longitudinal or the transverse antiferromagnetic long-range order exist. We find that the single-ion energy anisotropy has a strong influence on the critical value of the spin coupling constant between the one-dimensional integer-spin chains. Qualitatively, our results agree with the previous ones obtained by the mean-field theory and hence, reestablish the conclusions on a mathematically rigorous basis.

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.

The field-induced transition in one-dimensional

S=1

Heisenberg antiferromagnets with single-ion anisotropy in the presence of a transverse magnetic field is obtained on the basis of the Schwinger-boson mean-field theory. The behaviors of the specific heat and susceptibility as functions of temperature as well as the applied transverse field are explored, which are found to be different from the results obtained under a longitudinal field. The anomalies of the specific heat at low temperatures, which might be indicative of a field-induced transition from a Luttinger liquid phase to an ordered phase, are explicitly uncovered under the transverse field. A schematic phase diagram is proposed. The theoretical results are compared with experimental observations.