Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Magnetics

A renormalization-group study of the Haldane gap antiferromagnets

C. Y. Pan, H. Q. Lin

Published Jan 1, 1995• 3 citations
Publisher

Abstract

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.

DOI
10.1109/20.489887

Related papers

RENORMALIZATION GROUP STUDY OF THE ANISOTROPIC AND ALTERNATING HEISENBERG ANTIFERROMAGNETS

H. Q. Lin, C. Y. Pan

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.

Le Journal de Physique Colloques•Dec 1, 1988•1 citation

Renormalization-group study of high-spin Heisenberg antiferromagnets

C. Y. Pan, Xiyao Chen

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.

Physical review. B, Condensed matter•Dec 1, 1987•19 citations

SPIN-1/2 TWO-DIMENSIONAL ANISOTROPIC HEISENBERG ANTIFERROMAGNETS

C. Y. Pan

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.

International Journal of Modern Physics B•Sep 1, 1989•4 citations

Ground-State Phase Diagram of S = 2 Heisenberg Chains with Alternating Single-Site Anisotropy

Kazuo Hida

The ground-state phase diagram of $S=2$ antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-$D$, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.

arXiv:1310.8586•Journal of the Physical Society of Japan•Feb 14, 2014•3 citations

Equal-time correlations in Haldane-gap antiferromagnets

Erik Schwartz Sørensen, Ian K. Affleck

The S=1 antiferromagnetic Heisenberg chain both with and without single-ion anisotropy is studied. Using the recently proposed density-matrix renormalization-group technique of White, we calculate the energy gaps as well as several different correlation functions. The two gaps, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{\ensuremath{\parallel}}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{\ensuremath{\perp}}}$, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions derived from the nonlinear \ensuremath{\sigma} model and a free-boson model. We also study the S=1/2 excitations that occur at the ends of open chains; in particular we study the behavior associated with open boundary conditions, using a model of S=1/2 spins coupled to the free bosons.

arXiv:cond-mat/9402035•Physical review. B, Condensed matter•Jun 1, 1994•83 citations

GROUND-STATE ENERGY OF THE SPIN-1/2 TWO-DIMENSIONAL ANTIFERROMAGNETIC HEISENBERG MODEL

C. Y. Pan

The ground-state energy of the spin-1/2 two-dimensional antiferromagnetic Heisenberg model is obtained by a real space renormalization group method. A relative larger cluster (5×5) is used to improve the accuracy and a boundary theory is applied to extrapolate to the result which is in good agreement with the finite-size calculation and in fairly good agreement with the other available numerical estimates. How to further improve the calculation is discussed.

International Journal of Modern Physics B•Sep 1, 1989•1 citation
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 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.
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 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.
The ground-state phase diagram of S=2S=2S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-DDD, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
The S=1 antiferromagnetic Heisenberg chain both with and without single-ion anisotropy is studied. Using the recently proposed density-matrix renormalization-group technique of White, we calculate the energy gaps as well as several different correlation functions. The two gaps, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{\ensuremath{\parallel}}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{\ensuremath{\perp}}}$, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions derived from the nonlinear \ensuremath{\sigma} model and a free-boson model. We also study the S=1/2 excitations that occur at the ends of open chains; in particular we study the behavior associated with open boundary conditions, using a model of S=1/2 spins coupled to the free bosons.