Electronic Hamiltonian and antiferromagnetic interactions inLa2CuO4

A many-body Hamiltonian for ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ with ab initio parameters is solved numerically using embedded-cluster approximations. The results give an antiferromagnetic insulator with a 2–3 eV energy gap, consistent with spectroscopic measurements, NMR chemical shifts, and the spin-wave velocity. The Néel state has a significant frustration due to second-neighbor interactions, $J_2$/$J_1$≊5%–8%. Two competing states are found for holes introduced by doping, with primarily in-plane oxygen $p_{\sigma }$ and out-of-plane oxygen $p_z$ character.