Non-perturbative series expansion of Green's functions: The Anatomy of Resonant Inelastic X-Ray Scattering in Doped Hubbard Model

TL;DR

This paper introduces a non-perturbative, divergence-free series expansion method for Green's functions, applied to analyze RIXS in doped Hubbard models, revealing dominant local spin excitations in cuprates.

Contribution

The paper develops a novel non-perturbative series expansion technique for Green's functions, enabling detailed analysis of RIXS in strongly correlated systems.

Findings

Local spin excitations dominate RIXS spectral weight in cuprates.

The method effectively separates contributions from different degrees of freedom.

The approach provides clear selection rules for polarization channels.

Abstract

We present a non-perturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.