impurityModel

Official Resources

• Homepage: https://github.com/JohanSchott/impurityModel
• Documentation: https://github.com/JohanSchott/impurityModel
• Source Repository: https://github.com/JohanSchott/impurityModel
• License: MIT License

Overview

impurityModel is a Julia/Python-based exact diagonalization (ED) solver for the Anderson impurity model. It is specialized for simulating core-level spectroscopies (like XPS, XAS, RIXS) where finite-size effects of ED are less critical or where multiplet effects are dominant. It allows for the accurate simulation of local many-electron physics in core-level spectroscopy, particularly for correlated materials like transition metal oxides.

Scientific domain: Quantum impurity models, Spectroscopy (XPS, XAS, RIXS) Target user community: Spectroscopists, DMFT researchers needing ED solvers

Theoretical Methods

• Anderson Impurity Model (AIM)
• Exact Diagonalization (Lanczos algorithm)
• Core-level spectroscopy simulation
• Charge-transfer multiplet theory
• Spin-orbit coupling

Capabilities (CRITICAL)

• Spectral Functions: Calculates static and dynamic correlation functions (Green's functions).
• Spectroscopy: Specialized for:
  • XPS: X-ray Photoemission Spectroscopy.
  • XAS: X-ray Absorption Spectroscopy (L-edges, K-edges).
  • RIXS: Resonant Inelastic X-ray Scattering (photon-in, photon-out).
• Hamiltonian: Flexible definition of impurity Hamiltonians including full Coulomb interaction matrix and bath hybridization.
• Finite T: Finite temperature calculations (via Lanczos).

Key Features

Lightweight ED:

• An efficient, lightweight alternative to heavy CT-QMC for problems suitable for ED (small bath sizes).
• Ideal for atomic-like limits and core-level physics where multiplets dominate.

Julia/Python Interface:

• Easy to define models and parameters.
• Scriptable analysis workflows.

Inputs & Outputs

• Input formats:
  • Model parameters (hopping t, interaction U, J, slater, hybridization V) defined in script.
• Output data types:
  • Spectra (Intensity vs Energy).
  • Ground state wavefunctions.

Interfaces & Ecosystem

• Standalone: Can be used standalone for spectroscopy simulation.
• Integration: Potentially interfaced as a solver for DMFT loops when bath sizes are small.

Performance Characteristics

• Cost: Exponential scaling with number of bath sites (typical ED limitation).
• Speed: Fast for small clusters standard in multiplet calculations.

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/JohanSchott/impurityModel
2. Literature: Standard application of Anderson Impurity Model to X-ray spectroscopy.

Verification status: ✅ VERIFIED

• Source code: OPEN (GitHub)
• Focus: ED solver for spectroscopy