3,721 research outputs found

    Zero-Temperature Configurations of Short Odd-Numbered Classical Spin Chains with Bilinear and Biquadratic Exchange Interactions

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    The lowest energy configurations of short odd open chains with classical spins are determined for antiferromagnetic bilinear and biquadratic nearest-neighbor exchange interactions. The zero field residual magnetization generates differences with the magnetic behavior of even chains, as the odd chain is like a small magnet for weak magnetic fields. The lowest energy configuration is calculated as a function of the total magnetization M, even for M less than the zero field residual magnetization. Analytic expressions and their proofs are provided for the threshold magnetic field needed to drive the system away from the antiferromagnetic configuration and the spin polar angles in its vicinity, when the biquadratic interaction is relatively weak. They are also given for the saturation magnetic field and the spin polar angles close to it. Finally, an analytic expression along with its proof is given for the maximum magnetization in zero magnetic field for stronger biquadratic interaction, where the lowest energy configuration is highly degenerate.Comment: 17 pages, 9 figure

    Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements

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    We investigate the rate of thermalization of local operators in the one-dimensional anisotropic antiferromagnetic Heisenberg model with next-nearest neighbor interactions that break integrability. This is done by calculating the scaling of the difference of the diagonal and canonical thermal ensemble values as function of system size, and by directly calculating the time evolution of the expectation values of the operators with the Chebyshev polynomial expansion. Spatial and spin symmetry is exploited and the Hamiltonian is divided in subsectors according to their symmetry. The rate of thermalization depends on the proximity to the integrable limit. When integrability is weakly broken thermalization is slow, and becomes faster the stronger the next-nearest neighbor interaction is. Three different regimes for the rate of thermalization with respect to the strength of the integrability breaking parameter are identified. These are shown to be directly connected with the relative strength of the low and higher energy difference off-diagonal operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close to the integrable limit the off-diagonal matrix elements peak at higher energies and high frequency fluctuations are important and slow down thermalization. Away from the integrable limit a strong low energy peak gradually develops that takes over the higher frequency fluctuations and leads to quicker thermalization.Comment: 11 pages, 9 figure

    Quantum magnetization discontinuities proportional in number to the spin ss in C60_{60}

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    The antiferromagnetic Heisenberg model on the fullerene C60_{60} in a magnetic field has 4s4s ground-state magnetization discontinuities as a function of the spin quantum number ss that disappear at the classical limit. The molecule can be seen as the fullerene C20_{20} with interpentagonal interactions that can be tuned to generate the discontinuities. The results show how spatial symmetry dictates the magnetic response of the IhI_h fullerene molecules.Comment: 13 pages, 4 figures, 11 table
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