Pseudo-Majorana functional renormalization for frustrated XXZ spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> models with field or magnetization along the spin-<mml:

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-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>Z</a:mi></a:math> 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 antiferromagnetic triangular lattice materials recently studied in experiments with applied magnetic fields: First, we numerically reproduce the magnetization data measured for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>CeMgAl</b:mi><b:mn>11</b:mn></b:msub><b:msub><b:mi mathvariant="normal">O</b:mi><b:mn>19</b:mn></b:msub></b:mrow></b:math> 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 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>Na</d:mi><d:mn>2</d:mn></d:msub><d:mi>BaCo</d:mi><d:msub><d:mrow><d:mo>(</d:mo><d:msub><d:mi>PO</d:mi><d:mn>4</d:mn></d:msub><d:mo>)</d:mo></d:mrow><d:mn>2</d:mn></d:msub></d:mrow></d:math> in good agreement with experiment.