Journal of the Physical Society of Japan

Correlation Length of theS=2Antiferromagnetic Heisenberg Chain

Naomichi Hatano, Masuo Suzuki

Published Apr 15, 1993• 30 citations

Abstract

Temperature dependence of the correlation length of the one-dimensional S =2 Heisenberg antiferromagnet is investigated numerically, to compare with those of the S =1/2, 1, 3/2 models. The correlation length of the S =2 model is found to be saturated to a value ξ -1 ≃0.012(2) as T →0, which confirms the Haldane conjecture. Combined with the estimate ξ -1 ≃0.16 of the S =1 model by other authors, the present estimate is well explained by ξ -1 ∼ S exp (-π S ).

DOI: 10.1143/jpsj.62.1346

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Journal of the Physical Society of JapanMay 15, 19876 citations

Journal of the Physical Society of Japan

Correlation Length of theS=2Antiferromagnetic Heisenberg Chain

Naomichi Hatano, Masuo Suzuki

Published Apr 15, 1993• 30 citations

Publisher

Abstract

DOI: 10.1143/jpsj.62.1346

Related papers

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K. Nomura, Miki Yamada

Physical review. B, Condensed matterApr 1, 199130 citations

Thermal Properties of Chains of Antiferromagnetically Coupled Spins with s = 1: Numerical Evidence of the Haldane Gap at Nonzero Temperatures

Thomas Delica, Klaas Kopinga, Hajo Leschke +1 more

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Low-temperature behavior of the correlation length and the susceptibility of the ferromagnetic quantum Heisenberg chain

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The renormalization-group recursion relations for the spin-S nearest-neighbor quantum Heisenberg ferromagnet recently derived by Chakravarty and the present author are analyzed in one dimension. It is found that the susecptibility \ensuremath{\chi} is given at low temperatures T by T\ensuremath{\chi}=${C}_{\ensuremath{\chi}}^{(0)}$( ${\mathrm{JS}}^{2}$ /T) [1+${C}_{\ensuremath{\chi}}^{(1)}$\ensuremath{\eta}+O(${\ensuremath{\eta}}^{2}$)], where J is the exchange coupling and the dimensionless expansion parameter \ensuremath{\eta} is given by \ensuremath{\eta}=${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}1}$(T/ ${\mathrm{JS}}^{3}$ ${)}^{1/2}$ . For the correlation length \ensuremath{\xi} we find (\ensuremath{\xi}/a)=${C}_{\ensuremath{\xi}}^{(0)}$( ${\mathrm{JS}}^{2}$ /T) [1+${C}_{\ensuremath{\xi}}^{(1)}$\ensuremath{\eta}+O(${\ensuremath{\eta}}^{2}$)], where a is the lattice spacing. The values of the coefficients ${C}_{\ensuremath{\chi}}^{(j)}$ and ${C}_{\ensuremath{\xi}}^{(j)}$ (j=0,1), have been determined by fitting the above expressions with Monte Carlo data obtained for the S=1/2 Heisenberg chain at temperatures as low as T/J=0.01.The renormalization-group recursion relations for the spin-S nearest-neighbor quantum Heisenberg ferromagnet recently derived by Chakravarty and the present author are analyzed in one dimension. It is found that the susecptibility \ensuremath{\chi} is given at low temperatures T by T\ensuremath{\chi}=${C}_{\ensuremath{\chi}}^{(0)}$(${\mathrm{JS}}^{2}$/T) [1+${C}_{\ensuremath{\chi}}^{(1)}$\ensuremath{\eta}+O(${\ensuremath{\eta}}^{2}$)], where J is the exchange coupling and the dimensionless expansion parameter \ensuremath{\eta} is given by \ensuremath{\eta}=${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}1}$(T/${\mathrm{JS}}^{3}$${)}^{1/2}$. For the correlation length \ensuremath{\xi} we find (\ensuremath{\xi}/a)=${C}_{\ensuremath{\xi}}^{(0)}$(${\mathrm{JS}}^{2}$/T) [1+${C}_{\ensuremath{\xi}}^{(1)}$\ensuremath{\eta}+O(${\ensuremath{\eta}}^{2}$)], where a is the lattice spacing. The values of the coefficients ${C}_{\ensuremath{\chi}}^{(j)}$ and ${C}_{\ensuremath{\xi}}^{(j)}$ (j=0,1), have been determined by fitting the above expressions with Monte Carlo data obtained for the S=1/2 Heisenberg chain at temperatures as low as T/J=0.01.

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Kiyomi Okamoto

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{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

{)}^{2}

, D\ensuremath{\gtrsim}0, and find that the Haldane and the large-D phase are separated by an XY phase. The string correlation function vanishes only in the D\ensuremath{\rightarrow}\ensuremath{\infty} limit and does not distinguish between the Haldane phase and the perturbative large-D phase. An analysis of the transition mechanism and of the S=2 phase diagram in the presence of easy-plane and exchange anisotropy, markedly different from the S=1 phase diagram, allow us to conjecture how the classical limit is reached from increasing integer spins. \textcopyright{} 1996 The American Physical Society.

{\mathrm{JS}}^{2}

/T) [1+${C}_{\ensuremath{\chi}}^{(1)}$\ensuremath{\eta}+O(${\ensuremath{\eta}}^{2}$)], where J is the exchange coupling and the dimensionless expansion parameter \ensuremath{\eta} is given by \ensuremath{\eta}=${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}1}$(T/

{\mathrm{JS}}^{3}

{)}^{1/2}

. For the correlation length \ensuremath{\xi} we find (\ensuremath{\xi}/a)=${C}_{\ensuremath{\xi}}^{(0)}$(

{\mathrm{JS}}^{2}

/T) [1+${C}_{\ensuremath{\xi}}^{(1)}$\ensuremath{\eta}+O(${\ensuremath{\eta}}^{2}$)], where a is the lattice spacing. The values of the coefficients ${C}_{\ensuremath{\chi}}^{(j)}$ and ${C}_{\ensuremath{\xi}}^{(j)}$ (j=0,1), have been determined by fitting the above expressions with Monte Carlo data obtained for the S=1/2 Heisenberg chain at temperatures as low as T/J=0.01.