  We investigate the role of non-local correlations in LiFeAs by exploring an
ab-initio-derived multi-orbital Hubbard model for LiFeAs via the Two-Particle
Self-Consistent (TPSC) approach. The multi-orbital formulation of TPSC
approximates the irreducible interaction vertex to be an orbital-dependent
constant, which is self-consistently determined from local spin and charge sum
rules. Within this approach, we disentangle the contribution of local and
non-local correlations in LiFeAs and show that in the local approximation one
recovers the dynamical-mean field theory (DMFT) result. The comparison of our
theoretical results to most recent angular-resolved photoemission spectroscopy
(ARPES) and de-Haas van Alphen (dHvA) data shows that non-local correlations in
LiFeAs are decisive to describe the measured spectral function $A(\vec
k,\omega)$, Fermi surface and scattering rates. These findings underline the
importance of non-local correlations and benchmark different theoretical
approaches for iron-based superconductors.
