Quantum Phase Classification Project

Project Overview

This project implements machine learning techniques to classify quantum phases in spin chain systems, based on correlation functions as feature vectors.

Models Implemented

The project includes three quantum spin chain models:

• XXZ chains with uniaxial single-ion anisotropy (H1)
• Bond alternating XXZ chain (H2)
• Bilinear biquadratic chain (H3)

Directory Structure

/
├── data/              # Generated correlation data CSVs
├── images/            # Generated figures from notebook analyses
├── correlators.py      # Implements correlation function calculations
├── data_generation.py  # Generates data from quantum models
├── hamiltonians.py     # Defines quantum Hamiltonians
├── main.ipynb         # Main analysis notebook
└── utils.py           # Helper functions and constants

Key Features

• Implementation of quantum spin chain Hamiltonians
• Correlation function calculations
• Data generation for different model parameters
• Machine learning phase classification using KNN
• PCA visualization of quantum phases

Dependencies

• NumPy
• SciPy
• Pandas
• Scikit-learn
• Matplotlib
• tqdm

Running data generation

The main script to compute correlation CSVs is data_generation.py. It uses multiprocessing to parallelize Hamiltonian diagonalizations and correlator evaluations.

Basic usage:

python data_generation.py [N] [n_cores] [H1 H2 H3]

• N — number of spins (default 8)
• n_cores — number of worker processes to spawn (default 2)
• Optional trailing arguments: list which Hamiltonians to generate (H1, H2, H3). Example: python data_generation.py 12 4 H1 H2

Outputs are written to data/H1/N=<N>.csv, data/H2/N=<N>.csv, data/H3/N=<N>.csv.

Notes about performance:

• Exact diagonalization scales badly with system size (matrix dimension grows as 3^N for spin-1). Keep N small (commonly 4, 8, 12 in this repo's data).
• When n_cores is larger than your available CPU count, the script reduces it automatically.

Author

Edgard Macena Cabral