Numerical study of resonant inelastic X-ray scattering at the oxygen $K$-edge in insulating cuprates

TL;DR

This study uses three computational methods to analyze RIXS spectra at the oxygen K-edge in insulating cuprates, revealing detailed momentum-dependent excitations and differences between theoretical approaches.

Contribution

It provides a comparative analysis of RIXS spectra using CPT, HFA, and ED methods within the three-band Hubbard model, highlighting their differences in momentum dependence.

Findings

CPT captures the overall momentum dependence of ZRS and charge-transfer excitations.

HFA shows different momentum dependencies compared to CPT.

ED analysis supports the spectral features and charge dynamics findings.

Abstract

We investigate resonant inelastic X-ray scattering (RIXS) at the O $K$-edge in insulating cuprates by means of three methods: cluster perturbation theory (CPT), Hartree--Fock approximation (HFA) and exact diagonalization (ED) method. We consider the three-band Hubbard model and show the overall momentum-dependence of the Zhang--Rice singlet (ZRS) excitation and charge-transfer excitation by the CPT combining with the perturbation scheme. A comparison of the RIXS spectra calculated using CPT and HFA reveals different momentum-dependencies through the changes in the properties of the upper Hubbard band and the ZRS band. These findings are supported by analyses using the ED method on the RIXS spectra and dynamical charge structure factor.