Comparison of 32-site exact-diagonalization results and ARPES spectral functions for the antiferromagnetic insulatorSr2CuO2Cl2

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 ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$. After presenting arguments justifying our extraction of $A(\mathbf{k},\omega )$ 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 neighbors, as well three-site, spin-dependent hopping, can indeed explain not only the dispersion relation, but also the quasiparticle lifetimes—only in the neighborhood of $\mathbf{k}=(\pi /2,0)$ do we find disagreement; (ii) an energy-dependent broadening function, $\Gamma \mathrm{}\left(E\right)={\Gamma }_0+AE$, is important in accounting for the incoherent contributions to the spectral functions.