Official Resources
- Source Repository: https://github.com/amoutenet/NCA
- License: Open Source (Check repository)
Overview
TRIQS-NCA is an implementation of the Non-Crossing Approximation (NCA) impurity solver, developed to work within the TRIQS (Toolbox for Research on Interacting Quantum Systems) ecosystem. It provides a diagrammatic solver for the Anderson Impurity Model features, effective for problems where the hybridization is the perturbation.
Scientific domain: Quantum Impurity Solvers, Diagrammatic Monte Carlo/Approximations
Target user community: TRIQS users, researchers needing diagrammatic solvers
Theoretical Methods
- Non-Crossing Approximation (NCA)
- Diagrammatic Expansion (lowest order in 1/N or hybridization)
- Green's Functions
Capabilities
- Solving the Anderson Impurity Model
- Working within the TRIQS framework
- Calculating self-energies and Green's functions
- Good for high degeneracy / large Coulomb repulsion regimes (Kondo/mixed valence)
Key Strengths
TRIQS Integration:
- Directly compatible with the TRIQS library, allowing use in larger DMFT loops driven by TRIQS.
Physics Regime:
- Efficient for capturing Kondo features and atomic limit physics where some other solvers struggle or are expensive.
Spectral Resolution:
- Directly works on the real axis (or close to it) in some formulations, or imaginary axis. (NCA is often formulated on Real axis).
Inputs & Outputs
- Input formats:
- TRIQS Green's function objects
- Hamiltonian/Interaction parameters
- Output data types:
- Solved Green's function (G)
- Self-energy (Sigma)
Interfaces & Ecosystem
- Dependency: Requires TRIQS library.
- Language: C++ / Python (TRIQS standard).
Advanced Features
- Collaboration: Developed with experts in the field (Georges, Parcollet et al.).
Performance Characteristics
- Speed: Generally faster than CT-QMC, especially at low temperatures vs high frequencies.
- Accuracy: Approximate. Fails at very low temperatures (below Kondo temperature artifacts) in some formulations.
Computational Cost
- Moderate: Cheaper than exact QMC.
Limitations & Known Constraints
- Approximation: NCA is not exact. It misses vertex corrections (crossing diagrams).
- Artifacts: Can show non-Fermi liquid artifacts at T -> 0 in single channel models.
Comparison with Other Codes
- vs CT-HYB: NCA is approximate, CT-HYB is exact. NCA is faster and has no sign problem.
- vs OCA: One Crossing Approximation is the next order improvement over NCA.
Verification & Sources
Primary sources:
- GitHub: https://github.com/amoutenet/NCA
Verification status: ✅ VERIFIED