Accelerating Resonant Spectroscopy Simulations Using Multi-Shifted Bi-Conjugate Gradient

Abstract

Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide essential insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multi-shifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials.

10 pages, 5 figures

References in corpus (29)

• Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
• Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O(6+x)
• Inelastic Light Scattering From Correlated Electrons
• Isospin Dynamics in Sr2IrO4 : Forging Links to Cuprate Superconductivity
• Persistence of magnetic excitations in La2-xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal
• Resonant X-rays at the Cu L-edge as a momentum dependent probe of the magnetic excitation spectrum in cuprates
• Three dimensional collective charge excitations in electron-doped cuprate superconductors
• Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering
• Electronic and magnetic excitations in La${}_3$Ni${}_2$O${}_7$
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• Probing light-driven quantum materials with ultrafast resonant inelastic X-ray scattering
• Magnetic Excitations in La2CuO4 probed by Indirect Resonant Inelastic X-ray Scattering
• Using RIXS to uncover elementary charge and spin excitations in correlated materials
• Raman signature of the U(1) Dirac spin-liquid state in spin-1/2 kagome system
• New light on magnetic excitations: indirect resonant inelastic X-ray scattering on magnons
• Theoretical Understanding of Photon Spectroscopies in Correlated Materials In and Out of Equilibrium
• Evolution of spin excitations from bulk to monolayer FeSe
• Unraveling the Nature of Charge Excitations in La${}_2$CuO${}_4$ with Momentum-Resolved Cu $K$-edge Resonant Inelastic X-ray Scattering
• EDRIXS: An open source toolkit for simulating spectra of resonant inelastic x-ray scattering
• Exploring Quantum Materials with Resonant Inelastic X-Ray Scattering
• Uncovering selective excitations using the resonant profile of indirect inelastic x-ray scattering in correlated materials: Observing two-magnon scattering and relation to the dynamical structure factor
• Computing Resonant Inelastic X-Ray Scattering Spectra Using The Density Matrix Renormalization Group Method
• Multi-spinon and holon excitations probed by resonant inelastic x-ray scattering on doped one-dimensional antiferromagnets
• Paradeisos: a perfect hashing algorithm for many-body eigenvalue problems
• Emergence of Quasiparticles in a Doped Mott Insulator
• Distinguishing finite momentum superconducting pairing states with two-electron photoemission spectroscopy
• Angle-Resolved Pair Photoemission Theory for Correlated Electrons
• Entanglement Witness for Indistinguishable Electrons using Solid-State Spectroscopy
• Detection of chiral spin fluctuations driven by frustration in Mott insulators