Free Fermion Library Documentation

Welcome to the Free Fermion Library documentation! This library provides comprehensive tools for working with free fermion quantum systems, including combinatorial functions, graph theory algorithms, and quantum physics utilities.

Contents:

Overview

The Free Fermion Library is organized into four main modules:

ff_lib: Core quantum physics and linear algebra functions
ff_combinatorics: Combinatorial matrix functions (pfaffians, hafnians, etc.)
ff_graph_theory: Graph algorithms and visualization for planar graphs
ff_utils: Common utility functions

Key Features

Core Quantum Physics Functions

Jordan-Wigner transformations (Dirac and Majorana fermions)
Symplectic free-fermion diagonalization
Gaussian state generation and manipulation
Fermionic correlation matrix computations
Wick’s theorem implementation

Combinatorial Functions

Pfaffian computation via combinatorial formula
Hafnian computation
Permanent and determinant calculations
Sign of permutation functions

Graph Theory Algorithms

Pfaffian ordering algorithm (FKT algorithm) for planar graphs
Perfect matching algorithms
Planar graph generation and visualization
Dual graph construction

Utility Functions

Matrix cleaning and formatting
Random bitstring generation
Direct sum operations
Pretty printing with numerical precision control

Quick Start

Installation:

pip install free-fermion-lib

Basic usage:

import numpy as np
from ff import *

# Generate Jordan-Wigner operators for 3 sites
n_sites = 3
alphas = jordan_wigner_alphas(n_sites)

# Create a simple Hamiltonian matrix
A = np.random.random((n_sites, n_sites))
A = A + A.T  # Make symmetric
H = build_H(n_sites, A)

# Generate a Gaussian state
rho = generate_gaussian_state(n_sites, H, alphas)

# Compute correlation matrix
gamma = compute_2corr_matrix(rho, n_sites, alphas)