  We investigate a 2+1-D interacting Dirac semimetal with onsite flavor SU(2)
symmetry. Topological considerations imply that the skyrmions in the
flavor-symmetry-breaking phase carry electron quantum numbers, motivating a
dual bosonized low energy description in terms of two complex scalars coupled
to an abelian Chern-Simons field. We propose that the transition between a
nearby Chern insulator and the flavor symmetry-broken phase is a bicritical
point in the bosonized description, and also suggest that the
Gross-Neveu-Heisenberg (GNH) transition between the Dirac semimetal and the
flavor symmetry-broken phase is a tricritical point. Heuristically, the dual
description corresponds to the gap closing of fermionic skyrmions. We discuss
implications and potential issues with our proposal, and motivated from it,
perform extensive unbiased Determinantal Quantum Monte Carlo (DQMC) simulations
on a lattice regularized Hamiltonian for the GNH transition, extending
previously available results. We compare DQMC results with the estimates in the
proposed dual from available perturbative renormalization group results. We
also numerically demonstrate the presence of fermionic skyrmions in the
symmetry-broken phase of our lattice model.
