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Comparison of 32-site exact diagonalization results and ARPES spectral functions for the AFM insulator $Sr_2CuO_2Cl_2$

We explore the success of various versions of the one-band t-J model in explaining the full spectral functions found in angle-resolved photoemission spectra for the prototypical, quasi two-dimensional, tetragonal, antiferromagnetic insulator $Sr_2CuO_2Cl_2$. After presenting arguments justifying our extraction of $A(k,ω)$ from the experimental data, we rely on exact-diagonalization results from studies of a square 32-site lattice, the largest cluster for which such information is presently available, to perform this comparison. Our work leads us to believe that (i) a one-band model that includes hopping out to third-nearest neighbours, as well three-site, spin-dependent hopping, can indeed explain not only the dispersion relation, but also the quasiparticle lifetimes -- only in the neighbourhood of $k = (π/2,0)$ do we find disagreement; (ii) an energy-dependent broadening function, $Γ(E) = Γ_0 + A E$, is important in accounting for the incoherent contributions to the spectral functions.