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The orbital structure of the quantum Hall ferromagnetic states in thezero-energy Landau level in chiral multilayer graphene (AB, ABC, ABCA, etc.\stackings) is determined by the exchange interaction with all levels, includingdeep-lying states in the Dirac sea. This exchange field favors orbitallycoherent states with a U(1) orbital symmetry if the filling factor $\nu$ is nota multiple of the number of layers. If electrons fill the orbital sector of afixed spin/valley component to one-half, e.g., at $\nu=\pm3,\pm1$ in thebilayer and at $\nu=\pm2,\pm6$ in the ABCA four-layer, there is a transition toan $Z_2\times$U(1) manifold. For weak interaction, the structure in thezero-energy Landau band compensates for the different exchange interaction onthe sublattices in the Landau orbitals; on the other side, the ground statecomes in two copies that distribute charge on the sublattices differently. Weexpect a sequence of similar bifurcations in multilayers of Bernal stacking.

Particle-hole symmetry and bifurcating ground state manifold in the quantum Hall ferromagnetic states of multilayer graphene