Speaker
Description
The 3D chiral Heisenberg model is a theory of relativistic fermions in three spacetime dimensions with SU(2) symmetry. We simulate it numerically as a lattice field theory using domain wall fermions and locate the phase transition corresponding to spontaneous SU(2)$\to$U(1) breaking. This phase transition belongs to the large "chiral Heisenberg" universality class, containing among others the semi-metal - Mott insulator transition of the (2+1)D Hubbard model on the honeycomb lattice. Our simulation results are considerably removed from estimates obtained from simulations performed in (2+1)D, but align more closely with analytic estimates obtained using 3D covariant field theory. The tension between the two approaches is evident, but it is unclear what exactly is causing this discrepancy and, more importantly, how it can be eliminated in the future. We encourage the community to contemplate this apparent limitation of numerical simulations. We also present first results for the anti-symmetric matrix-valued fermion correlator which turns out to be technically very challenging to analyse.