  The interplay between topology and electronic correlation effects offers a
rich avenue for discovering emergent quantum phenomena in condensed matter
systems. In this work, starting from the Weyl-Hubbard model, we investigate the
quantum Hall effect to explore the consequence of onsite Hubbard repulsion on
nontrivial Weyl band topology in the presence of an external magnetic field.
Within the Gutzwiller projected wavefunction method, we find the system to
undergo multiple topological phase transitions, including two distinct Weyl
phases with a different number of Weyl node pairs and a trivial narrow band
insulator, by tuning on-site Coulomb interaction. Interestingly, these two Weyl
phases can be identified by the sign of their chiral Landau levels. The
possible experimental signature of these topological phases and correlation
effects is provided by the magnetic-field dependent quantum Hall conductivity
within the Kubo response theory.
