EDRIXS

Official Resources

• Homepage: https://github.com/EDRIXS/edrixs
• Documentation: https://nsls-ii.github.io/edrixs/
• Source Repository: https://github.com/EDRIXS/edrixs
• PyPI: https://pypi.org/project/edrixs/
• License: BSD-3-Clause

Overview

EDRIXS (Exact Diagonalization for Resonant Inelastic X-ray Scattering) is an open-source toolkit designed for simulating X-ray Absorption Spectroscopy (XAS), Resonant Inelastic X-ray Scattering (RIXS), and Resonant Magnetic X-ray Scattering (RMXS). Built on exact diagonalization (ED) of model Hamiltonians, it is particularly suited for studying strongly correlated materials where local interactions play a critical role. EDRIXS combines a high-performance Fortran 90 core for heavy numerical tasks with a flexible Python interface for setup and post-processing, allowing users to handle complex interactions like spin-orbit coupling, crystal structure fields, and Coulomb interactions within a user-defined cluster.

Scientific domain: Strongly correlated electron systems, X-ray spectroscopy (XAS, RIXS, RMXS), Transition metal oxides, f-electron systems Target user community: Researchers in condensed matter physics and physical chemistry focusing on spectroscopic analysis of correlated materials

Theoretical Methods

• Exact Diagonalization (ED): Solves many-body Hamiltonians for eigenvalues and eigenvectors
• Lanczos Algorithm: Efficient iterative method for finding ground and excited states
• Krylov Subspace Techniques: Used for calculating spectral functions and response functions
• Cluster Perturbation Theory: For treating extended systems beyond small clusters
• Model Hamiltonians:
  • Anderson Impurity Model
  • Hubbard Model parameters
  • Crystal Field Theory
  • Spin-Orbit Coupling
  • Slater-Condon parameters for Coulomb interactions
• Wannier Functions: Integration with Wannier90 to define realistic model parameters from DFT

Capabilities

• Spectroscopy Simulation:
  • X-ray Absorption Spectroscopy (XAS)
  • Resonant Inelastic X-ray Scattering (RIXS)
  • Resonant Magnetic X-ray Scattering (RMXS)
• Hamiltonian Solvers:
  • Fortran Solver: MPI-parallelized for large Hilbert spaces (based on ARPACK)
  • Python Solver: Pure Python implementation for small systems (Hilbert space < ~10,000)
• Complex Interaction Modeling:
  • Full multiplet theory
  • Charge transfer effects
  • Low-symmetry crystal fields
• Transition Amplitudes: Calculation of non-spin-flip and spin-flip processes

Key Strengths

• Hybrid Architecture: Combines the ease of use of Python with the performance of Fortran/MPI.
• ** versatility**: Applicable to single atoms, small clusters, and impurity models.
• Spectroscopy Focus: Specialized for simulating modern resonant X-ray experiments.
• Integration: Seamlessly utilizes parameters from DFT+Wannier90 or DMFT calculations.
• Open Source: Community-driven development with BSD licensing.

Inputs & Outputs

• Inputs:
  • Electronic structure parameters (hopping integrals, Coulomb U, J)
  • Geometry and cluster definitions
  • Incident/outgoing photon energies and polarizations
  • Slater-Condon parameters
• Outputs:
  • Spectral functions (Intensity vs Energy)
  • Eigenvalues and Eigenvectors
  • Expectation values of operators
  • Transition amplitudes

Interfaces & Ecosystem

• Python Interface: comprehensive API for workflow management, pre-processing, and plotting (import edrixs).
• Wannier90: Can read and use Wannier functions to construct realistic tight-binding Hamiltonians.
• DFT Integration: Bridges first-principles calculations (e.g., via Wannier90) with many-body model simulations.
• DMFT: Compatible with Dynamical Mean-Field Theory workflows for impurity problems.

Performance Characteristics

• Parallelization: MPI-based parallelism for the Fortran solver allows scaling to multi-core clusters.
• Efficiency: Optimized Lanczos and Krylov solvers for sparse matrices.
• Scalability: Limited by the exponential scaling of the Hilbert space size typical of Exact Diagonalization methods.
• Memory: Efficient handling of sparse Hamiltonian matrices.

Limitations & Known Constraints

• System Size: Restricted to small clusters or impurity models due to exponential scaling of ED.
• Python Solver: "Pure" Python solver is limited to small Hilbert spaces (< 10,000 basis states); larger problems require the Fortran/MPI backend.
• Approximation: Cluster methods may miss long-range correlations present in bulk systems (though CPT helps).

Comparison with Other Codes

• vs. Quanty: Both perform multiplet calculations; EDRIXS is open-source (BSD) and emphasizes Python/Wannier integration.
• vs. ALPS: ALPS is a general framework for lattice models; EDRIXS is specifically optimized for X-ray spectroscopy workflows (XAS/RIXS).
• vs. CTM4XAS: CTM4XAS is often GUI-based; EDRIXS offers a programmable Python environment for advanced users.

Application Areas

• Transition Metal Oxides: Studying d-orbital physics, magnetism, and charge transfer.
• Lanthanides/Actinides: Modeling f-electron systems with strong spin-orbit coupling.
• High-Tc Superconductors: Analyzing RIXS spectra to understand magnetic and orbital excitations.
• Quantum Materials: Investigating topological and correlated phases via spectroscopic signatures.

Community and Support

• Source: Hosted on GitHub with issue tracking and contributions.
• Documentation: Hosted on GitHub Pages (NSLS-II).
• Development: Originally developed at Brookhaven National Laboratory (COMSCOPE project).

Verification & Sources

• Official Website: https://github.com/EDRIXS/edrixs
• Documentation: https://nsls-ii.github.io/edrixs/
• Primary Publication: Wang, Y. L., et. al., "EDRIXS: An open source toolkit for simulating RIXS spectra...". Comput. Phys. Commun. 243, 151 (2019).
• Verification status: ✅ VERIFIED
  • Code is active and open source.
  • Validated against standard atomic multiplet codes and experimental data.