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

A Nocera,G Alvarez,S Johnston,U Kumar,E Dagotto,N Kaushal

doi:10.1038/s41598-018-29218-8

Abstract

We present a method for computing the resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address this 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 CuO4 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 main features of the magnetic excitations probed by RIXS only after a uniform scaling of the spectra is made.

Highlights

The results for a L = 16 sites t-J chain are presented in Supplementary Note I. (We provide a similar comparison for a four-plaquette multi-orbital cluster in Supplementary Note II.) Our density matrix renormalization group (DMRG)
Using our DMRG algorithm, we can compute the RIXS spectra on 1D clusters much larger than those accessible to state-of-the-art exact diagonalization (ED) methods
We modeled the magnetic excitations probed by RIXS at the Cu L-edge in 1D antiferromagnets on the largest cluster sizes to date

Summary

Group Method

By using DMRG to address this 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 used to obtain RIXS spectra on cluster sizes well beyond stateof-the-art ED techniques. We present an efficient algorithm to compute the dynamical correlation function representing the RIXS scattering cross section with DMRG directly in frequency space. We apply this approach to computing the Cu L-edge RIXS spectra of a quasi-1D corner-shared cuprate (e.g., Sr2CuO3, see Fig. 1b), a geometry that is challenging for ED calculations due to significant finite size effects[3,6,8]. The precise method for doing this is discussed in Supplementary Note IV

Computational Procedure

Concluding Remarks

Methods