exactdiag

Official Resources

• Homepage: https://github.com/mikeschmitt/exactdiag
• Source Repository: https://github.com/mikeschmitt/exactdiag
• License: MIT License

Overview

exactdiag is a Python package for performing exact diagonalization of fermionic many-body systems. Uniquely, it leverages Numba to Just-In-Time (JIT) compile critical inner loops, allowing it to achieve performance close to compiled languages like C++ or Fortran while efficient Python scripting. It focuses on the Anderson Impurity Model and Hubbard models, providing tools for Green's functions and spectral densities.

Scientific domain: Correlated Electrons, DMFT Impurity Solvers Target user community: Python users requiring fast ED for small fermionic clusters

Theoretical Methods

• Fermionic ED: Creation/Annihilation operator algebra treating fermion signs correctly.
• Lehmann Representation: Calculation of dynamical quantities ($G(\omega)$) via spectral expansion.
• Linear Operators: Uses scipy.sparse.linalg.LinearOperator to avoid storing full matrices when possible.

Capabilities (CRITICAL)

• Numba Acceleration: JIT compilation of Hamiltonian action on state vectors.
• Model Support: Specialized for Single-Impurity Anderson Models (SIAM) and Hubbard chains/clusters.
• Spectral Functions: Efficient computation of Zero-temperature Green's functions.
• Symmetries: Can exploit particle number and spin conservation.

Key Features

Performance:

• Python + Numba: The ease of Python with the speed of machine code.
• Sparse Algebra: Interface with generic SciPy eigensolvers (ARPACK).

Usability:

• Object-Oriented: Classes for Basis, Hamiltonian, and GreenFunction.

Inputs & Outputs

• Input formats:
  • Python scripts defining hopping $t_{ij}$ and interaction $U_{ijkl}$.
• Output data types:
  • Arrays of frequencies and spectral weights.

Interfaces & Ecosystem

• Dependencies: Python, NumPy, SciPy, Numba.
• Integration: Can be used as a lightweight solver in a Python-based DMFT loop.

Workflow and Usage

import exactdiag as ed
# Define basis
basis = ed.Basis(nsites=4, nup=2, ndn=2)
# Create Hamiltonian
H = ed.Hamiltonian(basis, ...parameters...)
# Diagnose
evals, evecs = H.diagonalize()

Performance Characteristics

• Speed: Significantly faster than pure Python/NumPy implementations due to Numba.
• Memory: Standard ED limits apply, but sparse formulation helps.

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/mikeschmitt/exactdiag

Verification status: ✅ VERIFIED

• Source code: OPEN (MIT)
• Focus: Numba-accelerated ED.