Magnetic materials are typically described in terms of the Heisenberg model, which provides an accurate account of thermodynamic properties when combined with first principles calculations. This approach is usually based on an energy mapping between density functional theory and a classical Heisenberg model. However, for two-dimensional systems the the eigenenergies of the Heisenberg model may differ significantly from the classical approximation, which leads to modified expressions for exchange parameters. Here we demonstrate that density functional theory yields local magnetic moments that are in accordance with strongly correlated anti-ferromagnetic eigenstates of the Heisenberg Hamiltonian implying that density functional theory provides a description of these states that conforms with the quantum mechanical eigenstates of the model. We then provide expressions for exchange parameters based on a proper eigenstate mapping to the Heisenberg model and find that they are typically reduced by 5-15 % compared to a classical analysis. Finally, we calculate the corrections to critical temperature for magnetic ordering for a previously predicted set of two-dimensional insulators and find that the inclusion of quantum effects may reduce the predictions of critical temperatures by up to 10 %.

中文翻译：

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二维磁性材料的第一原理海森堡模型：量子校正对交换耦合的重要性


磁性材料通常用海森堡模型来描述，该模型与第一原理计算相结合，可以准确地描述热力学性质。这种方法通常基于密度泛函理论和经典海森堡模型之间的能量映射。然而，对于二维系统，海森堡模型的本征能可能与经典近似有很大不同，这导致交换参数的表达式被修改。在这里，我们证明密度泛函理论产生的局部磁矩与海森堡哈密顿量的强相关反铁磁本征态一致，这意味着密度泛函理论提供了对这些状态的描述，符合模型的量子力学本征态。然后，我们根据海森堡模型的正确本征态映射提供交换参数的表达式，并发现与经典分析相比，它们通常减少 5-15%。最后，我们计算了先前预测的一组二维绝缘体的磁排序临界温度的修正，并发现包含量子效应可能会将临界温度的预测降低多达 10%。