Resonant inelastic x-ray scattering spectra of spinon, doublon, and quarton excitations of a spin-$\frac{1}{2}$ antiferromagnetic Heisenberg trimer chain

TL;DR

This study combines numerical and theoretical methods to analyze RIXS spectra of a spin-1/2 antiferromagnetic Heisenberg trimer chain, revealing fractionalized and collective excitations and proposing mechanisms for their experimental detection.

Contribution

It introduces a comprehensive approach to interpret RIXS spectra of trimer chains, identifying spinon, doublon, and quarton excitations and their formation mechanisms.

Findings

Single-particle continua match spinon, doublon, quarton energy levels.

Two-particle continua arise from combined single-particle excitations.

Excitations are detectable within current RIXS resolution at both $L$- and $K$-edges.

Abstract

We investigate the excitation spectra of a spin-1/2 antiferromagnetic Heisenberg trimer spin chain by employing a combination of numerical and theoretical techniques. Utilizing the Krylov-space correction-vector method in density matrix renormalization group (DMRG), we calculate both the direct and indirect resonant inelastic x-ray scattering (RIXS) spectra for the trimer spin chain. To interpret the observed features in the RIXS spectra, we perform a theoretical perturbative analysis to compute the energy dispersions which are then utilized to determine the density of states (DOS) for both the single-particle and the two-particle excitation spectra. Our results show that the single-particle continua of the direct RIXS spectrum align with the energy levels observed in the DOS spectra of spinon, doublon, and quarton excitations. Furthermore, the two-particle continua are revealed in the indirect RIXS process, where all possible single particle excitations combine to form the various two-particle excitations of the trimer spin chain. Based on our calculations, we propose the RIXS mechanism of generating the fractionalized (spinon) and collective (doublon and quarton) excitations in the trimer spin chain at both the $L$-edge and the $K$-edge, including discussing the interplay of these excitations in the RIXS spectrum for various trimer coupling strength. The computed energy range of the excitations suggest the possibility of experimental detection at both the $L$-edge and the $K$-edge within the current capabilities of RIXS instrumentation resolution.