Exact diagonalization (ED) code for working with Fermion systems and spin models on lattices

The Fermion models supported include Fermi-Hubbard systems and spinless Fermions with nearest-neighbor interactions. The spin models supported include the Heisenberg model, Ising model, and an extended Rydberg Ising model relevant to rydberg atoms.

This project also includes tools for reducing the size of the matrices which must be diagonalized by taking advantage of symmetries of the Hamiltonians. The approach adopted here is described in detail in ed-symmetries.tex and many useful references can be found both here and in bibliography.bib.

Installation

git clone https://github.com/ptbrown1729/exact_diag.git
cd exact_diag
pip install .

If you would like to modify the code, then use the -e option so it is not necessary to reinstall the package for your changes to take effect

pip install -e .

Package contents

ed_base.py

This file defines a base class for use with different exact diagonalization models. This class defines basic functions such as taking expectation values, calculating partition functions, calculating Green's functions, etc.

ed_fermions.py

This file defines a class for working with Fermion systems, including spinless fermions of Fermi-Hubbard type models. This class inherits from ed_base.py.

ed_spins.py

This file defines a class for working with spin systems, including Heisenberg, Ising, and Rydberg Ising. This class inherits from ed_base.py

ed_geometry.py

This file implements a class for defining clusters of sites, either using a specific lattice setup or an arbitrary geometry

ed_symmetry.py

This file implements symmetry operations and functions for creating projectors for reducing the Hamiltonians using these symmetry operations. This can allow diagonalization of much larger systems.

ed_nlce.py

This file implements cluster generation tools. Combining these clusters with the exact diagonalization code allows an easy implementation of the numerical linked cluster expansion (NLCE)

fermi_gas.py

functions for evaluating properties of a non-interacting Fermi gas, including equation of state, compressibility, spin correlations (for a two component gas), etc. Useful for comparing with Fermi-Hubbard model results.

greens_fns.py

Some tools for working with Green's functions, and transforming between various representations

examples

This directory contains various examples which make use of the exact diagonalization code

unittests

This directory contains various unittests for comparing exact diagonalization results with published data, and checking that the symmetry operators work appropriately. To test the code in ed_geometry.py, navigate to the unittests folder and run

python -m unittest geom_unittest.py 

cluster

This directory contains code that was used run exact diagonalizations scripts on Princeton Physics Feynman cluster using Slurm

Documentation

Documentation is generated from function docstrings and the files in doc using sphinx. To build the html version, navigate to docs and run

make html

Then open docs/_build/html/index.html in your browser