Multiloop pseudofermion functional renormalization for quantum spin systems: Application to the spin-1/2 kagome Heisenberg model

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.

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).

https://arxiv.org/abs/2011.01268