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arXiv 2407.09401cond-mat.str-el
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驯服受挫量子磁体中的自旋磁化率:平均场形式与量子-经典对应的近似本质

Taming spin susceptibilities in frustrated quantum magnets: Mean-field form and approximate nature of the quantum-to-classical correspondence

Benedikt Schneider, Björn Sbierski

AI总结:

本文利用重求和自旋图解微扰理论解析证明量子-经典对应在四阶弱破缺,并揭示静态关联函数可由重整化平均场形式高精度近似。

摘要:

在受挫磁性中,经验发现的量子-经典对应(QCC)将量子自旋-$1/2$模型的实空间静态磁化率模式与其在某一升高温度下计算的经典对应物相匹配。这一令人困惑的关系是通过在二维和三维中的粗线图蒙特卡罗模拟观察到的。匹配在误差棒范围内,并且似乎在低至比交换耦合$J$小约一个数量级的最低可及温度$T$下仍然有效。在此,我们采用重求和自旋图解微扰理论,解析地证明QCC在$J/T$的四阶处发生弱破缺,并给出经典温度与量子温度之间的近似映射。我们的处理进一步揭示,QCC表明静态关联函数可以以一种简单的重整化平均场形式被惊人准确地近似。我们对迄今为止在QCC背景下讨论的所有模型说明了这一点,包括最近一个$S=1$材料$\mathrm{K}_2\mathrm{Ni}_2(\mathrm{SO}_4)_3$的例子。平均场形式的成功可追溯到部分图解抵消。

英文摘要:

In frustrated magnetism, the empirically found quantum-to-classical correspondence (QCC) matches the real-space static susceptibility pattern of a quantum spin-$1/2$ model with its classical counterpart computed at a certain elevated temperature. This puzzling relation was observed via bold line diagrammatic Monte Carlo simulations in dimensions two and three. The matching was within error bars and seemed valid down to the lowest accessible temperatures $T$ about an order of magnitude smaller than the exchange coupling $J$. Here, we employ resummed spin diagrammatic perturbation theory to show analytically that the QCC breaks weakly at fourth order in $J/T$ and provide the approximate mapping between classical and quantum temperatures. Our treatment further reveals that QCC is an indication of the surprising accuracy with which static correlators can be approximated by a simple renormalized mean-field form. We illustrate this for all models discussed in the context of QCC so far, including a recent example of the $S=1$ material $\mathrm{K}_2\mathrm{Ni}_2(\mathrm{SO}_4)_3$. The success of the mean-field form is traced back to partial diagrammatic cancellations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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