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Physical review. B, Condensed matter

Renormalization-group study of high-spin Heisenberg antiferromagnets

C. Y. Pan, Xiyao Chen

Published Dec 1, 1987• 19 citations
Publisher

Abstract

An even-site block renormalization-group method is applied to the spin-1 and spin-(3/2 anisotropic or alternating Heisenberg antiferromagnets. In the spin-1 case it shows an energy gap \ensuremath{\Delta} \ensuremath{\simeq}0.368 166 and ground-state energy ${E}_{0}$/NJ\ensuremath{\simeq}1.449 724, which are in good agreement with the recent Monte Carlo results. In the spin-(3/2 case it shows an energy excitation behavior similar to that in the spin-(1/2 case. Therefore, our study tends to support Haldane's conjecture. In addition, a possible novel property of the spin-1 Heisenberg antiferromagnet has been predicted.

DOI
10.1103/physrevb.36.8600

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An even-site block renormalization-group method is applied to the spin-1 and spin-(3/2 anisotropic or alternating Heisenberg antiferromagnets. In the spin-1 case it shows an energy gap \ensuremath{\Delta} \ensuremath{\simeq}0.368 166 and ground-state energy E0{E}_{0}E0​/NJ\ensuremath{\simeq}1.449 724, which are in good agreement with the recent Monte Carlo results. In the spin-(3/2 case it shows an energy excitation behavior similar to that in the spin-(1/2 case. Therefore, our study tends to support Haldane's conjecture. In addition, a possible novel property of the spin-1 Heisenberg antiferromagnet has been predicted.
A real space renormalization group method is applied to study the properties of the anisotropic and alternating Heisenberg antiferromagnets with spin 1/2, 1 and 3/2. To improve the accuracy of the numerical estimates larger spin cluster is used. The ground state energy and the energy gap are obtained. For the case of S = 1 at Heisenberg point, the ground state energy per site is E (0)/N = -1.4021 ± 0.0005 and the energy gap is 0.4097 ± 0.0005, in excellent agreement with a recent Monte Carlo calculation. For the cases of spin 1/2 and 3/2 the energy gap is absent. Therefore our results are shown to support Haldane's conjecture. We briefly discuss the properties of the novel phase.
We have studied anisotropic Heisenberg antiferromagnets by using a real space renormalization-group analysis and exact diagonalization approach. For the spin-1 case, the ground-state energy and Haldane gap at the Heisenberg point are estimated, and they are in good agreement with that obtained by other methods. The critical point is identified where the gap phase changes into a gapless phase. For spin-2 case, the calculated Haldane gap supports a recent prediction suggested by a quantum O(N) nonlinear sigma model study.
A real space renormalization group method is applied to study the spin-1/2 two-dimensional anisotropic Heisenberg antiferromagnets. We carry out the calculation on a 5×5 cluster by using a variational approach. The ground-state energy per site is estimated as e0=−0.6845±0.0005 which is in good agreement with other numerical estimates. We also calculate the different ground state energies when anisotropy changes. By comparing with 3×3 cluster calculation the resulting threshold for long range order drops and the curve of the renormalization group parameter vs. anisotropy shows no hint of discontinuity over a wide range of anisotropic parameters. Hence, our calculation suggests that long-range order exists for the ground-state of the spin-1/2 Heisenberg antiferromagnets in two dimensions.
A zero-temperature renormalization group (RG) approach is applied to the one-dimensional, spin-1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest-lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin-1/2 XY dimerized chain.
The s=1 Heisenberg antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with J'\ensuremath{\ne}J at the center of an even-length open chain is considered. Using the density-matrix renormalization-group method we find that, for sufficiently strong or weak J', a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on s=1/2 chain-end excitations, both in the weak- and strong-coupling limit. In a region around the uniform limit, J'=J, no states are found with energy below the Haldane gap. Second, a s=1/2 impurity at the center of an otherwise even-length open chain is considered. The coupling to the s=1/2 impurity is varied. Bound states in the Haldane gap are found only for sufficiently weak (antiferromagnetic) coupling. For a s=1/2 impurity coupled with a strong (antiferromagnetic) bond, no states are found in the Haldane gap. Our results are in good qualitative agreement with recent experiments on doped NENP and Y2{\mathrm{Y}}_{2}Y2​BaNiO5{\mathrm{BaNiO}}_{5}BaNiO5​.