  We investigate a binary mixture of bosonic atoms loaded into a
state-dependent honeycomb lattice. For this system, the emergence of a
so-called twisted-superfluid ground state was experimentally observed in
[Soltan-Panahi et al., Nat. Phys. 8, 71 (2012)]. Theoretically, the origin of
this effect is not understood. We perform numerical simulations of an extended
Bose-Hubbard model adapted to the experimental parameters employing the
Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons. Our
results confirm the overall applicability of mean-field theory within the
relevant parameter range. Beyond this, we provide a detailed analysis of
correlation effects correcting the mean-field result. These have the potential
to induce asymmetries in single shot time-of-flight measurements, but we find
no indication of the patterns characteristic of the twisted superfluid. We
comment on the restrictions of our model and possible extensions.
