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

Physical review. B, Condensed matter

Numerical solution of the spin-2 Heisenberg antiferromagnetic chains using a projector method

Gang Sun

Published Apr 1, 1995• 26 citations
Publisher

Abstract

An efficient projector Monte Carlo method has been used to calculate the energies of the ground state and the first excited state, and hence the gap between them, of the spin-2 Heisenberg antiferromagnetic chains with linear sizes up to N=32. By direct extrapolation, we found that a Haldane gap exists, \ensuremath{\Delta}E=0.05, and the value of the ground-state energy per site is ${\mathit{e}}_{0}$=-4.7545 as N\ensuremath{\rightarrow}\ensuremath{\infty}.

DOI
10.1103/physrevb.51.8370

Related papers

Numerical Solution of the Spin-1 Heisenberg Antiferromagnetic Chains by Using a Projector Method

Gang Zheng Sun

Abstract An efficient projector Monte Carlo method has been used to calculate the energies of the ground state and the first excited state, and hence the gap between them, of the spin-1 Heisenberg antiferromagnetic chains with linear sizes up to <?CDATA $N=40$?> . We have computed them on chains up to <?CDATA $N=40$?> . We have found that the size-dependence of the ground state energy per site has the form <?CDATA $[e_0(N)-e_0]\sim 1/N^{5/2s}$?> , which implies that there is a gap between the ground state and the first excited state. The value of the ground state energy per site as <?CDATA $N\rightarrow \infty$?> is <?CDATA $e_0=-1.3996$?> . The direct extrapolation of <?CDATA $\Delta E(N)$?> also shows that a gap of <?CDATA $\Delta E=0.36$?> exists as <?CDATA $N\rightarrow \infty$?> .

Communications in Theoretical Physics•Sep 1, 1992•0 citations

Numerical Solution of the spin-$\frac {3}{2}$ Heisenberg Antiferromagnetic Chains Using a Projector Method

Gang Zheng Sun, Fu‐Cho Pu

An efficient projector method is used to calculate the energies of the ground state and the first excited state, and hence the energy gap between them, of the spin- Heisenberg antiferromagnetic chains with linear sizes up to . For the chains up to the exact results are obtained, and for longer chains up to they are estimated by imposing on Monte Carlo technique. It is found that the size dependence of the ground state energy per site has the form of , and the value of the ground state energy per site as is . Our results show that the energy gap trends to zero as , which is consistent with the rigorous proof.

Communications in Theoretical Physics•Mar 1, 1993•0 citations

Numerical Solution of the spin-$\frac {1}{2}$ Heisenberg Antiferromagnetic Chains Using a Projector Method

Gang Sun

An efficient projector method is proposed to calculate the energy gap between the ground, state and the first excited state of the spin- Heisenberg antiferromagnetic chains. We exactly computed the two lowest-lying energies for the magnetization and the lowest-lying energy for on chains up to 16 spins. The lowest-lying energy stat6 for is a singlet ground state. The second lowest-lying energy state for and the lowest-lying energy states for are triplet degenerate, which are the first excited energy states. We also imposed the Monte Carlo technique to estimate the lowest-lying energies for both and 1 on longer chains up to 32 spins. We found that the singlet-triplet energy gap trends to zero as .

Communications in Theoretical Physics•Sep 1, 1991•1 citation

Haldane Gap in the Spin-1/2 Double Chain Heisenberg Antiferromagnet -Numerical Diagonalization and Projector Monte Carlo Study-

Kazuo Hida

The properties of the spin-1/2 double chain Heisenberg antiferromagnet are studied by means of the numerical diagonalization and the projector Monte Carlo simulation. The model consists of the two spin 1/2 antiferromagnetic quantum Heisenberg chains coupled with each other via the ferromagnetic interchain coupling J ′ . It is shown that the first excited state has a gap for large enough J ′ . This gap continues to the Haldane gap in the limit J ′ →∞, where spins on the different chains form triplets on each site. On the other hand, the gap decreases rapidly between J ′ =1.0 and 0.6 and is undetectable for J ′ <0.6 within the present accuracy.

Journal of the Physical Society of Japan•Apr 15, 1991•78 citations

Monte Carlo calculation of elementary excitation of spin chains

Minoru Takahashi

An efficient Monte Carlo method is proposed to calculate the elementary excitation spectrum of quantum systems. The lowest energy with arbitrary momentum is obtained by the projector Monte Carlo method. This is applied to the spin-(1/2 and -1 Heisenberg antiferromagnetic chain with length 32. For the S=(1/2 case, the spectrum coincides completely with the spectrum of des Cloiseaux and Pearson. For the S=1 case, the spectrum has a gap at momentum \ensuremath{\pi} as was predicted by Haldane. The value of the gap coincides with the calculation of Nightingale and Blote. The spectrum satisfies a variational relation with the structure factor.

Physical Review Letters•May 8, 1989•202 citations

Gap of the linear spin-1 Heisenberg antiferromagnet: A Monte Carlo calculation

M. P. Nightingale, Henk W. J. Blöte

We have performed Monte Carlo calculations of the energies of several low-lying energy states of one-dimensional, spin-1 Heisenberg antiferromagnets with linear sizes up to n=32. Our results support Haldane's prediction that a gap exists in the excitation spectrum for n\ensuremath{\rightarrow}\ensuremath{\infty}. .AE

Physical review. B, Condensed matter•Jan 1, 1986•412 citations
An efficient projector Monte Carlo method has been used to calculate the energies of the ground state and the first excited state, and hence the gap between them, of the spin-2 Heisenberg antiferromagnetic chains with linear sizes up to N=32. By direct extrapolation, we found that a Haldane gap exists, \ensuremath{\Delta}E=0.05, and the value of the ground-state energy per site is e0{\mathit{e}}_{0}e0​=-4.7545 as N\ensuremath{\rightarrow}\ensuremath{\infty}.
Abstract An efficient projector Monte Carlo method has been used to calculate the energies of the ground state and the first excited state, and hence the gap between them, of the spin-1 Heisenberg antiferromagnetic chains with linear sizes up to <?CDATA N=40N=40N=40?> . We have computed them on chains up to <?CDATA N=40N=40N=40?> . We have found that the size-dependence of the ground state energy per site has the form <?CDATA [e0(N)−e0]∼1/N5/2s[e_0(N)-e_0]\sim 1/N^{5/2s}[e0​(N)−e0​]∼1/N5/2s?> , which implies that there is a gap between the ground state and the first excited state. The value of the ground state energy per site as <?CDATA N→∞N\rightarrow \inftyN→∞?> is <?CDATA e0=−1.3996e_0=-1.3996e0​=−1.3996?> . The direct extrapolation of <?CDATA ΔE(N)\Delta E(N)ΔE(N)?> also shows that a gap of <?CDATA ΔE=0.36\Delta E=0.36ΔE=0.36?> exists as <?CDATA N→∞N\rightarrow \inftyN→∞?> .
Numerical Solution of the spin-32\frac {3}{2}23​ Heisenberg Antiferromagnetic Chains Using a Projector Method
An efficient projector method is used to calculate the energies of the ground state and the first excited state, and hence the energy gap between them, of the spin- Heisenberg antiferromagnetic chains with linear sizes up to . For the chains up to the exact results are obtained, and for longer chains up to they are estimated by imposing on Monte Carlo technique. It is found that the size dependence of the ground state energy per site has the form of , and the value of the ground state energy per site as is . Our results show that the energy gap trends to zero as , which is consistent with the rigorous proof.
Numerical Solution of the spin-12\frac {1}{2}21​ Heisenberg Antiferromagnetic Chains Using a Projector Method
An efficient projector method is proposed to calculate the energy gap between the ground, state and the first excited state of the spin- Heisenberg antiferromagnetic chains. We exactly computed the two lowest-lying energies for the magnetization and the lowest-lying energy for on chains up to 16 spins. The lowest-lying energy stat6 for is a singlet ground state. The second lowest-lying energy state for and the lowest-lying energy states for are triplet degenerate, which are the first excited energy states. We also imposed the Monte Carlo technique to estimate the lowest-lying energies for both and 1 on longer chains up to 32 spins. We found that the singlet-triplet energy gap trends to zero as .
The properties of the spin-1/2 double chain Heisenberg antiferromagnet are studied by means of the numerical diagonalization and the projector Monte Carlo simulation. The model consists of the two spin 1/2 antiferromagnetic quantum Heisenberg chains coupled with each other via the ferromagnetic interchain coupling J ′ . It is shown that the first excited state has a gap for large enough J ′ . This gap continues to the Haldane gap in the limit J ′ →∞, where spins on the different chains form triplets on each site. On the other hand, the gap decreases rapidly between J ′ =1.0 and 0.6 and is undetectable for J ′ <0.6 within the present accuracy.
An efficient Monte Carlo method is proposed to calculate the elementary excitation spectrum of quantum systems. The lowest energy with arbitrary momentum is obtained by the projector Monte Carlo method. This is applied to the spin-(1/2 and -1 Heisenberg antiferromagnetic chain with length 32. For the S=(1/2 case, the spectrum coincides completely with the spectrum of des Cloiseaux and Pearson. For the S=1 case, the spectrum has a gap at momentum \ensuremath{\pi} as was predicted by Haldane. The value of the gap coincides with the calculation of Nightingale and Blote. The spectrum satisfies a variational relation with the structure factor.