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

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.

6+6 pages; 4+9 figures

References in corpus (8)

• Continuous-time Monte Carlo methods for quantum impurity models
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Bands, resonances, edge singularities and excitons in core level spectroscopy investigated within the dynamical mean field theory
• High-energy spin and charge excitations in electron-doped copper oxide superconductors
• Ultrashort Lifetime Expansion for Indirect Resonant Inelastic X-ray Scattering
• Crossover from Collective to Incoherent Spin Excitations in Superconducting Cuprates Probed by Detuned Resonant Inelastic X-ray Scattering
• Microscopic theory of resonant soft x-ray scattering in systems with charge order