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

摘要

The pseudofermion functional renormalization group (pf-FRG) is one of the fewnumerical approaches that has been demonstrated to quantitatively determine theordering tendencies of frustrated quantum magnets in two and three spatialdimensions. The approach, however, relies on a number of presumptions andapproximations, in particular the choice of pseudofermion decomposition and thetruncation of an infinite number of flow equations to a finite set. Here wegeneralize the pf-FRG approach to SU(N)-spin systems with arbitrary N anddemonstrate that the scheme becomes exact in the large-N limit. Numericallysolving the generalized real-space renormalization group equations forarbitrary N, we can make a stringent connection between the physically mostsignificant case of SU(2)-spins and more accessible SU(N) models. In a casestudy of the square-lattice SU(N) Heisenberg antiferromagnet, we explicitlydemonstrate that the generalized pf-FRG approach is capable of identifying theinstability indicating the transition into a staggered flux spin liquid groundstate in these models for large, but finite values of N. In a companion paper(arXiv:1711.02183) we formulate a momentum-space pf-FRG approach for SU(N) spinmodels that allows us to explicitly study the large-N limit and access thelow-temperature spin liquid phase.