Functional renormalization group approach to SU(N) Heisenberg models: Real-space renormalization group at arbitrary N

Abstract

The pseudofermion functional renormalization group (pf-FRG) is one of the few numerical approaches that has been demonstrated to quantitatively determine the ordering tendencies of frustrated quantum magnets in two and three spatial dimensions. The approach, however, relies on a number of presumptions and approximations, in particular the choice of pseudofermion decomposition and the truncation of an infinite number of flow equations to a finite set. Here we generalize the pf-FRG approach to $\mathrm{SU}(N)$-spin systems with arbitrary $N$ and demonstrate that the scheme becomes exact in the large-$N$ limit. Numerically solving the generalized real-space renormalization group equations for arbitrary $N$, we can make a stringent connection between the physically most significant case of SU(2) spins and more accessible $\mathrm{SU}(N)$ models. In a case study of the square-lattice $\mathrm{SU}(N)$ Heisenberg antiferromagnet, we explicitly demonstrate that the generalized pf-FRG approach is capable of identifying the instability indicating the transition into a staggered flux spin liquid ground state in these models for large, but finite, values of $N$. In a companion paper [Roscher et al., Phys. Rev. B 97, 064416 (2018)] we formulate a momentum-space pf-FRG approach for $\mathrm{SU}(N)$ spin models that allows us to explicitly study the large-$N$ limit and access the low-temperature spin liquid phase.