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As a minimal model to study charge transfer effects in a transition metal(TM) and Oxygen (OX) chain, we consider a one-dimensional chain with spinlessfermion with an alternating motif of site-pairs with nearest neighbor (NN)repulsion $U$ and uncorrelated site-pairs, separated by a charge transfer gap$\Delta$. We first show that while two holes added in a filled band of NNinteracting fermion in one dimension can stabilize to a two-hole bound pair,the bound pair delocalizes with a $U$-dependent bandwidth. In contrast, weestablish that the bandwidth of two holes added on a TM site-pair in a filledband is dramatically suppressed, realizing a `local' two-hole resonance (L2HR)at the same TM site-pair mimicking the AES phenomenology. Employing amemory-efficient exact numerical scheme and standard Lanczos-baseddiagonalization, we then study two-hole spectra for holes added at TMsite-pairs in partially filled bands. We analyze the multiple features thatarise in the two-hole spectra at partial filling of the ground state. Weuncover that in the strong $U$ limit, there is a filling-dependent$\Delta_{crit}$ above which the L2HR remains stable for any band-fillinggreater than 75\%. In this regime, the energy location of the L2HR provides adirect estimate of the correlation strength at TM site-pairs for partialfilling and is reminiscent of the Cini-Sawatzky theory for the filled bandcase. At 75\% band-filling, an abrupt redistribution of two-hole spectralweight destroys the L2HR regardless of $U$ or $\Delta$ values. We discuss therelevance of these nonperturbative results, obtained with full latticesymmetry, for understanding AES of partially filled bands in terms of thelocal-two-hole spectrum.

Charge transfer energy and band filling effects on two-hole Auger resonances in strongly correlated systems