  The fractional quantum anomalous Hall (FQAH) effect in rhombohedral
pentalayer graphene (PLG) has attracted significant attention due to its
potential for observing exotic quantum states. In this work, we present a
self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In
particular, we focus on the convergence of the Hartree-Fock calculation with
various reference fields and discuss the stability of the FQAH states in PLG.
We show that the so-called charge neutrality scheme provides an unambiguous
result for the Hartree-Fock calculation, as it ensures a convergence with
respect to the momentum cutoff. Based on the Hartree-Fock band structure, we
further carry out exact diagonalization calculations to explore the stability
of the FQAH states in PLG. Our work provides an improved and unified (minimal)
theoretical framework to understand the FQAH effect in rhombohedral PLG and
paves the way for future experimental and theoretical studies.
