We present a multiloop pseudofermion functional renormalization group
(pffRG) approach to quantum spin systems and its application to the
spin-1/2 Heisenberg model on the kagome lattice. At pure
nearest-neighbor coupling, the system shows indications for an algebraic
spin liquid through slower-than-exponential decay with distance for the
static spin susceptibility, while the pseudofermion self-energy develops
a pronounced low-energy power law. Methodologically, the pseudofermion
representation of spin models inherently yields a strongly interacting
system, and the quantitative reliability of a truncated fRG flow is a
priori unclear. We demonstrate convergence in loop order, which provides
further evidence for the internal consistency of the approach through
correspondence with the self-consistent parquet equations. In the
spin-liquid phase, the multiloop flow remains stable as the infrared
cutoff Λ is reduced down to below 1% of the microscopic exchange
interaction J. We also scrutinize the pseudofermion constraint of single
occupation per site, which is only fulfilled on average in pffRG.
Although fluctuations in the occupation number are not entirely
suppressed, we find that they do not affect the qualitative conclusions
drawn from the spin susceptibility.
Reference: Multiloop pseudofermion functional renormalization for quantum spin systems: Application to the spin-1/2 kagome Heisenberg model
J. Thoenniss, M. K. Ritter, F. B. Kugler, J. von Delft and M. Punk
arXiv:2011.01268 [cond-mat.str-el] (2020).