Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group

TL;DR

This paper uses advanced functional renormalization group techniques to analyze the critical behavior of the Heisenberg and chiral Heisenberg models, providing improved estimates and exploring universality class issues.

Contribution

It introduces a comprehensive truncation and computational approach that refines critical quantity estimates for both models, especially addressing the chiral case.

Findings

Heisenberg model fixed point aligns with previous estimates

Chiral model results still disagree with lattice studies

Questions remain about universality class equivalence

Abstract

We discuss the Heisenberg model and its chiral extension in an extended truncation with the help of functional methods. Employing computer algebra to derive the beta functions, and pseudo-spectral methods to solve them, we are able to go significantly beyond earlier approximations, and provide new estimates on the critical quantities of both models. The fixed point of the Heisenberg model is mostly understood, and our results are in agreement with estimates from various other approaches, including Monte Carlo and conformal bootstrap studies. By contrast, in the chiral case, the formerly known disagreement with lattice studies persists, raising the question whether actually the same universality class is described.