Computing Resonant Inelastic X-Ray Scattering Spectra Using The Density Matrix Renormalization Group Method

TL;DR

This paper introduces a DMRG-based method to compute RIXS spectra in one-dimensional systems, enabling analysis of larger clusters than previous exact diagonalization methods and providing insights into magnetic excitations in CuO chains.

Contribution

The authors develop a DMRG approach for RIXS spectra calculation, overcoming memory limitations of ED and allowing analysis of larger clusters and detailed comparison of models.

Findings

DMRG method successfully computes RIXS spectra for larger clusters.

Downfolded t-J model captures magnetic excitations after scaling.

Comparison between multi-orbital and t-J models validates the approach.

Abstract

We present a method for computing resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address the problem, we shift the computational bottleneck from the memory requirements associated with exact diagonalization (ED) calculations to the computational time associated with the DMRG algorithm. This approach is then used to obtain RIXS spectra on cluster sizes well beyond state-of-the-art ED techniques. Using this new procedure, we compute the low-energy magnetic excitations observed in Cu $L$-edge RIXS for the challenging corner shared CuO$_4$ chains, both for large multi-orbital clusters and downfolded $t$-$J$ chains. We are able to directly compare results obtained from both models defined in clusters with identical momentum resolution. In the strong coupling limit, we find that the downfolded $t$-$J$ model captures the features of the magnetic excitations probed by RIXS after a uniform scaling of the spectra is taken into account.