NCA_Standalone

This is a standalone implementation of the Non-Crossing Approximation (NCA) for solving quantum impurity problems, written in Python. Unlike the TRIQS-based version, this is a self-contained code, suitable for learning or specific lightw…

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Overview

This is a standalone implementation of the Non-Crossing Approximation (NCA) for solving quantum impurity problems, written in Python. Unlike the TRIQS-based version, this is a self-contained code, suitable for learning or specific lightweight applications without the full TRIQS dependency stack.

Reference Papers

Reference papers are not yet linked for this code.

Full Documentation

Official Resources

  • Source Repository: https://github.com/CorentinB78/NCA
  • License: MIT License
  • Language: Python

Overview

This is a standalone implementation of the Non-Crossing Approximation (NCA) for solving quantum impurity problems, written in Python. Unlike the TRIQS-based version, this is a self-contained code, suitable for learning or specific lightweight applications without the full TRIQS dependency stack.

Scientific domain: Quantum Impurity Solvers, Many-body Physics Target user community: Students, Researchers needing a light, pure-Python NCA solver

Theoretical Methods

  • Non-Crossing Approximation (NCA)
  • Resolvent Operator formalism
  • Pseudo-particle Green's functions
  • Integral equations for self-consistency

Capabilities

  • Impurity Solver: Solves the Single Impurity Anderson Model (SIAM).
  • Spectral Functions: Calculates impurity spectral functions $A(\omega)$.
  • Finite Parameters: Handles finite interaction $U$, impurity level $\epsilon_d$, and finite temperatures.
  • Hybridization: Accepts arbitrary hybridization functions $\Delta(\omega)$.

Key Strengths

Simplicity:

  • Pure Python implementation effectively lowers the barrier to entry.
  • Minimal dependencies (NumPy/SciPy).

Education:

  • Clear code structure for understanding the integral equations of NCA.

Inputs & Outputs

  • Input formats:
    • Python script configuration: U, ed, beta, Gamma (hybridization width/function).
  • Output data types:
    • Spectral densities (text files or arrays).
    • Occupancies.

Interfaces & Ecosystem

  • Standalone: Independent of heavy frameworks like TRIQS.
  • Integration: Can be imported as a Python module.

Performance Characteristics

  • Efficiency: NCA is computationally efficient compared to QMC, but slower than simple approximations like Hubbard-I.
  • Cost: Low execution time for typical single-impurity problems.

Limitations & Known Constraints

  • Approximation: NCA validity is limited (good for large N, high T, strong coupling; fails at low T Fermi liquid regime).
  • Features: Lacks multi-orbital support and advanced features of production codes.

Comparison with Other Codes

  • vs TRIQS-NCA: Lighter, standalone, easier to install.
  • vs ED: Continuous bath support, but approximate.

Verification & Sources

Primary sources:

  1. GitHub: https://github.com/CorentinB78/NCA

Verification status: ✅ VERIFIED

  • Source code: OPEN (Python)
  • Method: NCA

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