Pseudo-fermion functional renormalization group with magnetic fields

Abstract: 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 $\Lambda$. 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.