Temperature flow in pseudo-Majorana functional renormalization for quantum spins

Abstract

We implement the temperature flow scheme first proposed by Honerkamp and Salmhofer [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 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the simple cubic lattice, where our findings support claims of a vanishingly small nonmagnetic phase around the high frustration point ${J}_{2}=0.25{J}_{1}$. 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 nonmagnetic 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.