arXiv:cond-mat/9812012 · Physical Review Letters

Temperature-Dependent Spatial Oscillations in the Correlations of the XXZ Spin Chain

K. Fabricius, Andreas Klümper, Barry M. McCoy

Published Jun 28, 1999• 13 citations

Abstract

We study the correlation $〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉$ for the $\mathrm{XXZ}$ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.

DOI: 10.1103/physrevlett.82.5365

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arXiv:cond-mat/9812012 · Physical Review Letters

Temperature-Dependent Spatial Oscillations in the Correlations of the XXZ Spin Chain

K. Fabricius, Andreas Klümper, Barry M. McCoy

Published Jun 28, 1999• 13 citations

arXiv HTML PDF

Abstract

We study the correlation

〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉

for the

\mathrm{XXZ}

chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.

DOI: 10.1103/physrevlett.82.5365

Related papers

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Masamichi Nishino, Kazumitsu Sakai, Masahiro Shiroishi +1 more

A crossover phenomenon of the longitudinal spin–spin correlation function is investigated on the spin-1/2 XXZ chain in a magnetic field at finite temperatures. A commensurate–incommensurate transition of the correlation function in the asymptotic behaviour has been pointed out by Klumper et al in the framework of the quantum transfer matrix method. We show the field dependence and the anisotropy-constant dependence of the critical temperature by the quantum transfer matrix method. Using a quantum Monte Carlo method with the continuous time loop algorithm, we directly observe the commensurate–incommensurate transition. Detailed quantum Monte Carlo analyses for the longitudinal spin–spin correlation in both the high and low temperature regions are presented. Especially in the low temperature region, evaluating the precise distance dependence of the correlation function, we prove that the incommensurate oscillation has detectable amplitude, which has not been estimated before. We also estimate the phase factor of the incommensurate oscillation, which accurately coincides with the one from the quantum transfer matrix method.A crossover phenomenon of the longitudinal spin–spin correlation function is investigated on the spin-1/2 XXZ chain in a magnetic field at finite temperatures. A commensurate–incommensurate transition of the correlation function in the asymptotic behaviour has been pointed out by Klumper et al in the framework of the quantum transfer matrix method. We show the field dependence and the anisotropy-constant dependence of the critical temperature by the quantum transfer matrix method. Using a quantum Monte Carlo method with the continuous time loop algorithm, we directly observe the commensurate–incommensurate transition. Detailed quantum Monte Carlo analyses for the longitudinal spin–spin correlation in both the high and low temperature regions are presented. Especially in the low temperature region, evaluating the precise distance dependence of the correlation function, we prove that the incommensurate oscillation has detectable amplitude, which has not been estimated before. We also estimate the phase factor of the incommensurate oscillation, which accurately coincides with the one from the quantum transfer matrix method.

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We compute, by means of exact diagonalization of systems of $N=16$ and $18$ spins, the correlation function $〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉$ at nonzero temperature for the $\mathrm{XXZ}$ model with anisotropy $\ensuremath{\Delta}.$ In the gapless attractive region $\ensuremath{-}1<\ensuremath{\Delta}<0$ for fixed separation the temperature can always be made sufficiently low so that the correlation is always negative for $n\ensuremath{\ne}0.$ However we find that for sufficiently large temperatures and fixed separation or for fixed temperature greater than some ${T}_{0}(\ensuremath{\Delta})$ and sufficiently large separations the correlations are always positive. This sign changing effect has not been previously seen and we interpret it as a crossover from quantum to classical behavior.We compute, by means of exact diagonalization of systems of $N=16$ and $18$ spins, the correlation function $〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉$ at nonzero temperature for the $\mathrm{XXZ}$ model with anisotropy $\ensuremath{\Delta}.$ In the gapless attractive region $\ensuremath{-}1<\ensuremath{\Delta}<0$ for fixed separation the temperature can always be made sufficiently low so that the correlation is always negative for $n\ensuremath{\ne}0.$ However we find that for sufficiently large temperatures and fixed separation or for fixed temperature greater than some ${T}_{0}(\ensuremath{\Delta})$ and sufficiently large separations the correlations are always positive. This sign changing effect has not been previously seen and we interpret it as a crossover from quantum to classical behavior.

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arXiv:cond-mat/0408529Physical Review BMay 26, 200566 citations

We study the correlation

〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉

for the

\mathrm{XXZ}

We compute, by means of exact diagonalization of systems of

N=16

and

18

spins, the correlation function $〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉$ at nonzero temperature for the

\mathrm{XXZ}

model with anisotropy $\ensuremath{\Delta}.$ In the gapless attractive region $\ensuremath{-}1<\ensuremath{\Delta}<0$ for fixed separation the temperature can always be made sufficiently low so that the correlation is always negative for $n\ensuremath{\ne}0.$ However we find that for sufficiently large temperatures and fixed separation or for fixed temperature greater than some ${T}_{0}(\ensuremath{\Delta})$ and sufficiently large separations the correlations are always positive. This sign changing effect has not been previously seen and we interpret it as a crossover from quantum to classical behavior.

We study the heat conduction of the spin-

1∕2

XXZ

chain in finite magnetic fields where magnetothermal effects arise. Due to the integrability of this model, all transport coefficients diverge, signaled by finite Drude weights. Using exact diagonalization and mean-field theory, we analyze the temperature and field dependence of the thermal Drude weight for various exchange anisotropies under the condition of zero magnetization-current flow. First, we find a strong magnetic field dependence of the Drude weight, including a suppression of its magnitude with increasing field strength and a nonmonotonic field-dependence of the peak position. Second, for small exchange anisotropies and magnetic fields in the massless as well as in the fully polarized regime, the mean-field approach is in excellent agreement with the exact diagonalization data. Third, at the field-induced quantum critical line between the para- and ferromagnetic region, we propose a universal low-temperature behavior of the thermal Drude weight.