Temperature flow in pseudo-Majorana functional renormalization for quantum spins

We implement the temperature flow scheme first proposed by Honerkamp and Salmhofer in Phys.~Rev.~B 64, 184516 (2001) into the pseudo-Majorana functional renormalization group method for quantum spin systems. Since the renormalization group parameter in this approach is a physical quantity -- the temperature $T$ -- the numerical efficiency increases significantly compared to more conventional renormalization group parameters, especially when computing finite temperature phase diagrams. We first apply this method to determine the finite temperature phase diagram of the $J_1$-$J_2$ Heisenberg model on the simple cubic lattice where our findings support claims of a vanishingly small nonmagnetic phase around the high frustration point $J_2=0.25J_1$. Perhaps most importantly, we find the temperature flow scheme to be advantageous in detecting finite temperature phase transitions as, by construction, a phase transition is never encountered at an artificial, unphysical cutoff parameter. Finally, we apply the temperature flow scheme to the dipolar XXZ model on the square lattice where we find a rich phase diagram with a large non-magnetic regime down to the lowest accessible temperatures. Wherever a comparison with error-controlled (quantum) Monte Carlo methods is applicable, we find excellent quantitative agreement with less than $5\%$ deviation from the numerically exact results.