Pseudo-Majorana functional renormalization for frustrated XXZ spin-1/2 models with field or magnetization along the spin-Z direction at finite temperature

The numerical study of high-dimensional frustrated quantum magnets remains a challenging problem. Here we present an extension of the pseudo-Majorana functional renormalization group to spin-1/2 XXZ type Hamiltonians with field or magnetization along spin-Z direction at finite temperature. We consider a $U(1)$ symmetry-adapted fermionic spin representation and derive the diagrammatic framework and its renormalization group flow equations. We discuss benchmark results and application to two anti-ferromagnetic triangular lattice materials recently studied in experiments with applied magnetic fields: First, we numerically reproduce the magnetization data measured for CeMgAl$_{11}$O$_{19}$ confirming model parameters previously estimated from inelastic neutron spectrum in high fields. Second, we showcase the accuracy of our method by studying the thermal phase transition into the spin solid up-up-down phase of Na$_2$BaCo(PO$_4$)$_2$ in good agreement with experiment.