Optimality of Hartree-Fock global minima for ED FQAH states in rhombohedral pentalayer graphene

Determine whether, in rhombohedral pentalayer graphene, selecting the global minimum of the Hartree–Fock mean-field energy as the basis for band projection invariably yields the most energetically favorable fractional quantum anomalous Hall ground state under subsequent exact diagonalization, or whether non-global/constrained Hartree–Fock solutions can produce lower-energy fractional quantum anomalous Hall states.

Background

In rhombohedral pentalayer graphene, many studies first use a Hartree–Fock approximation to isolate an effective quasiparticle conduction band and then perform exact diagonalization at fractional fillings to search for fractional quantum anomalous Hall states. However, because the Hartree–Fock solution can depend on filling and can substantially alter wavefunctions and Chern numbers, it is not obvious that the Hartree–Fock ground state (the global minimum of the mean-field energy) provides the best basis for subsequent exact diagonalization.

The authors highlight a conceptual issue concerning how to couple Hartree–Fock and exact diagonalization: whether they should be treated as separate steps or integrated self-consistently, and specifically whether choosing the Hartree–Fock global minimum necessarily leads to the energetically optimal many-body fractional quantum anomalous Hall state. This motivates their proposal to view Hartree–Fock primarily as a generator of basis states and to compare unconstrained and constrained Hartree–Fock inputs for exact diagonalization.