The pseudo-fermion functional renormalization group is generalized to treat spin Hamiltonians with finite magnetic fields, enabling its application to arbitrary spin lattice models with linear and bilinear terms in the spin operators. We discuss in detail an efficient numerical implementation of this approach making use of the system's symmetries. Particularly, we demonstrate that the inclusion of small symmetry-breaking magnetic seed fields regularizes divergences of the susceptibility at magnetic phase transitions. This allows the investigation of spin models within magnetically ordered phases at $T=0$ in the physical limit of vanishing renormalization group parameter $\mathrm{\Lambda }$. We explore the capabilities and limitations of this method extension for Heisenberg models on the square, honeycomb, and triangular lattices. While the zero-field magnetizations of these systems are systematically overestimated, the types of magnetic orders are correctly captured, even if the local orientations of the seed field are chosen differently than the spin orientations of the realized magnetic order. Furthermore, the magnetization curve of the square lattice Heisenberg antiferromagnet shows good agreement with error controlled methods. In the future, the inclusion of magnetic fields in the pseudo-fermion functional renormalization group, which is also possible in three-dimensional spin systems, will enable a variety of additional interesting applications such as the investigation of magnetization plateaus.

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具有磁场的伪费米子泛函重整化群

伪费米子泛函重正化群被推广到处理具有有限磁场的自旋哈密顿量，使其能够应用于自旋算子中具有线性和双线性项的任意自旋晶格模型。我们详细讨论了利用系统对称性的该方法的有效数值实现。特别是，我们证明了包含小的对称破缺磁种子场可以调节磁相变磁化率的发散。这允许在磁有序相内研究自旋模型$\mathrm{时间}=0$重整化群参数消失的物理极限$\mathrm{\Lambda }$。我们探索了这种方法在方形、蜂窝和三角形格子上扩展海森堡模型的能力和局限性。虽然这些系统的零场磁化强度被系统地高估，但磁序的类型被正确捕获，即使种子场的局部方向选择与实现的磁序的自旋方向不同。此外，方晶格海森堡反铁磁体的磁化曲线与误差控制方法表现出良好的一致性。未来，将磁场包含在赝费米子泛函重正化群中（这在三维自旋系统中也是可能的）将实现各种其他有趣的应用，例如磁化平台的研究。