arXiv:cond-mat/9904170 · Physica A Statistical Mechanics and its Applications

Spin dynamics of quantum and classical Heisenberg dimers

Detlef Mentrup, Jürgen Schnack, Marshall Luban

Published Oct 1, 1999• 31 citations

arXiv HTML PDF

DOI: 10.1016/s0378-4371(99)00239-3

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arXiv:cond-mat/9904170 · Physica A Statistical Mechanics and its Applications

Spin dynamics of quantum and classical Heisenberg dimers

Detlef Mentrup, Jürgen Schnack, Marshall Luban

Published Oct 1, 1999• 31 citations

arXiv HTML PDF

DOI: 10.1016/s0378-4371(99)00239-3

Related papers

Spin Dynamics of Heisenberg Chains

T. Schneider, E. Stoll

Modern problems in condensed matter sciencesJan 1, 19861 citation

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arXiv:cond-mat/9612013Europhysics Letters (EPL)Jan 20, 199728 citations

Dynamics of the one-dimensional Heisenberg spin system

Alf Sjölander

Lecture notes in physicsJan 1, 19790 citations

Spin and dimer correlations forS=1 bilinear-biquadratic antiferromagnetic Heisenberg chains

J. J. Deisz

Using the world-line quantum Monte Carlo method, we calculate the spin 〈 ${\mathit{S}}_{\mathit{R}}^{\mathit{z}}$ ${\mathit{S}}_{0}^{\mathit{z}}$ 〉 and dimer 〈( ${\mathbf{S}}_{0}$ \ensuremath{\cdot} ${\mathbf{S}}_{1}$ )( ${\mathbf{S}}_{\mathit{R}}$ \ensuremath{\cdot} ${\mathbf{S}}_{\mathit{R}+1}$ )〉 correlation functions for the S=1 biquadratic Heisenberg antiferromagnetic chain. These results show the relevance of the Affleck-Kennedy-Lieb-Tasaki state for describing the nonclassical behavior of the S=1 antiferromagnetic Heisenberg model. We also include results for S=3/2 and 2, which show the inhibition of staggered dimerization as the classical limit (S\ensuremath{\rightarrow}\ensuremath{\infty}) is approached, where N\'eel order is favored.Using the world-line quantum Monte Carlo method, we calculate the spin 〈${\mathit{S}}_{\mathit{R}}^{\mathit{z}}$${\mathit{S}}_{0}^{\mathit{z}}$〉 and dimer 〈(${\mathbf{S}}_{0}$\ensuremath{\cdot}${\mathbf{S}}_{1}$)(${\mathbf{S}}_{\mathit{R}}$\ensuremath{\cdot}${\mathbf{S}}_{\mathit{R}+1}$)〉 correlation functions for the S=1 biquadratic Heisenberg antiferromagnetic chain. These results show the relevance of the Affleck-Kennedy-Lieb-Tasaki state for describing the nonclassical behavior of the S=1 antiferromagnetic Heisenberg model. We also include results for S=3/2 and 2, which show the inhibition of staggered dimerization as the classical limit (S\ensuremath{\rightarrow}\ensuremath{\infty}) is approached, where N\'eel order is favored.

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Classical dynamics of the antiferromagnetic Heisenberg S = 1 2 spin ladder

David Dahlbom, Jinu Thomas, Steven Johnston +2 more

We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the $S=1/2$ ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite-size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high-temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule, following D. Dahlbom et al. [Phys. Rev. B 109, 014427 (2024)]. We anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly coupled dimers, situations that remain challenging for alternative numerical methods.We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the $S=1/2$ ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite-size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high-temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule, following D. Dahlbom et al. [Phys. Rev. B 109, 014427 (2024)]. We anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly coupled dimers, situations that remain challenging for alternative numerical methods.

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Spin Dynamics of Linear Heisenberg Magnetic Chains

F. B. McLean, Martin Blume

Physical review. B, Solid stateJun 1, 197328 citations

Using the world-line quantum Monte Carlo method, we calculate the spin 〈

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

{\mathit{S}}_{0}^{\mathit{z}}

〉 and dimer 〈(

{\mathbf{S}}_{0}

\ensuremath{\cdot}

{\mathbf{S}}_{1}

)(

{\mathbf{S}}_{\mathit{R}}

\ensuremath{\cdot}

{\mathbf{S}}_{\mathit{R}+1}

)〉 correlation functions for the S=1 biquadratic Heisenberg antiferromagnetic chain. These results show the relevance of the Affleck-Kennedy-Lieb-Tasaki state for describing the nonclassical behavior of the S=1 antiferromagnetic Heisenberg model. We also include results for S=3/2 and 2, which show the inhibition of staggered dimerization as the classical limit (S\ensuremath{\rightarrow}\ensuremath{\infty}) is approached, where N\'eel order is favored.

We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the

S=1/2

ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite-size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high-temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule, following D. Dahlbom et al. [Phys. Rev. B 109, 014427 (2024)]. We anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly coupled dimers, situations that remain challenging for alternative numerical methods.