Physical review. B, Condensed matter

Spin-correlation functions of theS=1Heisenberg-Ising chain by the large-cluster-decomposition Monte Carlo method

K. Nomura

Published Nov 1, 1989• 39 citations

Abstract

We study the spin-correlation functions of the one-dimensional S=1 antiferromagnetic Heisenberg-Ising model by the large-cluster-decomposition Monte Carlo method. It is found that this model shows a second-order transition at the anisotropy parameter ${\ensuremath{\lambda}}_{c}$=1.167\ifmmode\pm\else\textpm\fi{}0.007. The obtained critical exponents (\ensuremath{\eta}=0.253\ifmmode\pm\else\textpm\fi{}0.002, \ensuremath{\beta}=0.126\ifmmode\pm\else\textpm\fi{}0.007, \ensuremath{\nu}=0.98\ifmmode\pm\else\textpm\fi{}0.02) strongly suggest that this transition belongs to the same universality class as the two-dimensional Ising model.

DOI: 10.1103/physrevb.40.9142

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Physical review. B, Condensed matter

Spin-correlation functions of theS=1Heisenberg-Ising chain by the large-cluster-decomposition Monte Carlo method

K. Nomura

Published Nov 1, 1989• 39 citations

Publisher

Abstract

{\ensuremath{\lambda}}_{c}

=1.167\ifmmode\pm\else\textpm\fi{}0.007. The obtained critical exponents (\ensuremath{\eta}=0.253\ifmmode\pm\else\textpm\fi{}0.002, \ensuremath{\beta}=0.126\ifmmode\pm\else\textpm\fi{}0.007, \ensuremath{\nu}=0.98\ifmmode\pm\else\textpm\fi{}0.02) strongly suggest that this transition belongs to the same universality class as the two-dimensional Ising model.

DOI: 10.1103/physrevb.40.9142

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Spin correlation function of theS=1antiferromagnetic Heisenberg chain by the large-cluster-decomposition Monte Carlo method

K. Nomura

Physical review. B, Condensed matterAug 1, 198997 citations

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Satoshi Ejima, Florian Lange, Holger Fehske

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Shoji Yamamoto

Low-temperature properties of S=1 antiferromagnetic Heisenberg chains with alternating interaction, scrH= ${\mathit{Jtsum}}_{\mathit{i}}$ [1-(-1 ${)}^{\mathit{i}}$ \ensuremath{\delta}] ${\mathrm{S}}_{\mathit{i}}$ \ensuremath{\cdot} ${\mathrm{S}}_{\mathit{i}+1}$ , are studied by a quantum Monte Carlo method. Spatial distributions of the spin correlation function 〈 ${\mathit{S}}_{1}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 and the local magnetic moment 〈 ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 are visualized as a function of \ensuremath{\delta}. The continuous phase transition at \ensuremath{\delta}=0.25, which was indicated by several authors, is confirmed by the \ensuremath{\delta} dependence of the low-lying level structure, the divergence of the correlation length, and also the collapse of the edge states. The critical exponent \ensuremath{\eta}, governing the power-law decay of the spin correlation function, is estimated to be 0.99\ifmmode\pm\else\textpm\fi{}0.05. The present result raises a possibility that the variety of quantum spin chains including not only the half-odd-integer-S ones but also the integer-S ones may be described in terms of the generic critical theory.Low-temperature properties of S=1 antiferromagnetic Heisenberg chains with alternating interaction, scrH=${\mathit{Jtsum}}_{\mathit{i}}$[1-(-1${)}^{\mathit{i}}$\ensuremath{\delta}]${\mathrm{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathrm{S}}_{\mathit{i}+1}$, are studied by a quantum Monte Carlo method. Spatial distributions of the spin correlation function 〈${\mathit{S}}_{1}^{\mathit{z}}$${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 and the local magnetic moment 〈${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 are visualized as a function of \ensuremath{\delta}. The continuous phase transition at \ensuremath{\delta}=0.25, which was indicated by several authors, is confirmed by the \ensuremath{\delta} dependence of the low-lying level structure, the divergence of the correlation length, and also the collapse of the edge states. The critical exponent \ensuremath{\eta}, governing the power-law decay of the spin correlation function, is estimated to be 0.99\ifmmode\pm\else\textpm\fi{}0.05. The present result raises a possibility that the variety of quantum spin chains including not only the half-odd-integer-S ones but also the integer-S ones may be described in terms of the generic critical theory.

Physical review. B, Condensed matterOct 1, 199519 citations

{\ensuremath{\lambda}}_{c}

c=1/2

c = 1 / 2 , which terminates at a critical end-point where

c=7/10

c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find

\beta =1/8

β = 1 / 8 (1/24),

\nu =1

ν = 1 (5/9), and

\eta =1/4

η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.

{)}^{\mathit{r}}

c/${\mathit{r}}^{\mathrm{\ensuremath{\eta}}}$-

{\mathit{c}}_{1}

{\mathit{r}}^{2}

for large distance r. The power \ensuremath{\eta} depends on the Ising anisotropy, and \ensuremath{\eta}=0.405 at XY point and \ensuremath{\eta}=1.062 at Heisenberg point. For the two-dimensional square lattice, there is long-range staggered magnetization, and the dependence of magnetization on Ising anisotropy is given. For the crossover from one-dimensional linear chain to two-dimensional square lattice, we find that the disorder-order transition occurs as long as the interchain coupling is introduced. We believe that our method gives a unified approach to the long-range behavior of spin correlations in low-dimensional spin-1/2 antiferromagnets.

Low-temperature properties of S=1 antiferromagnetic Heisenberg chains with alternating interaction, scrH=

{\mathit{Jtsum}}_{\mathit{i}}

[1-(-1

{)}^{\mathit{i}}

\ensuremath{\delta}]

{\mathrm{S}}_{\mathit{i}}

\ensuremath{\cdot}

{\mathrm{S}}_{\mathit{i}+1}

, are studied by a quantum Monte Carlo method. Spatial distributions of the spin correlation function 〈

{\mathit{S}}_{1}^{\mathit{z}}

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

〉 and the local magnetic moment 〈

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

〉 are visualized as a function of \ensuremath{\delta}. The continuous phase transition at \ensuremath{\delta}=0.25, which was indicated by several authors, is confirmed by the \ensuremath{\delta} dependence of the low-lying level structure, the divergence of the correlation length, and also the collapse of the edge states. The critical exponent \ensuremath{\eta}, governing the power-law decay of the spin correlation function, is estimated to be 0.99\ifmmode\pm\else\textpm\fi{}0.05. The present result raises a possibility that the variety of quantum spin chains including not only the half-odd-integer-S ones but also the integer-S ones may be described in terms of the generic critical theory.