  Using local density approximation plus dynamical mean-field theory
(LDA+DMFT), we have computed the valence band photoelectron spectra of highly
popular multiferroic BiFeO$_{3}$. Within DMFT, the local impurity problem is
tackled by exact diagonalization (ED) solver. For comparison, we also present
result from LDA+U approach, which is commonly used to compute physical
properties of this compound. Our LDA+DMFT derived spectra match adequately with
the experimental hard X-ray photoelectron spectroscopy (HAXPES) and resonant
photoelectron spectroscopy (RPES) for Fe 3$d$ states, whereas the other
theoretical method that we employed failed to capture the features of the
measured spectra. Thus, our investigation shows the importance of accurately
incorporating the dynamical aspects of electron-electron interaction among the
Fe 3$d$ orbitals in calculations to produce the experimental excitation
spectra, which establishes BiFeO$_{3}$ as a strongly correlated electron
system. The LDA+DMFT derived density of states (DOSs) exhibit significant
amount of Fe 3$d$ states at the energy of Bi lone-pairs, implying that the
latter is not as alone as previously thought in the spectral scenario. Our
study also demonstrates that the combination of orbital cross-sections for the
constituent elements and broadening schemes for the calculated spectral
function are pivotal to explain the detailed structures of the experimental
spectra.
