Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group

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.

10 pages, 5 figures; v2: matches journal version

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• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
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• Fermion-induced quantum criticality with two length scales in Dirac systems
• Infinite order quantum-gravitational correlations
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• Fermionic criticality with enlarged fluctuations in Dirac semimetals
• Loop calculations for models of graphene
• Lattice Field Theory Analysis of the Chiral Heisenberg Model