Qsymm

Symmetry finder and symmetric Hamiltonian generator

qsymm is an open-source Python library that makes symmetry analysis simple.

It automatically generates model Hamiltonians from symmetry constraints and finds the full symmetry group of your Hamiltonian.

Check out the introductory example notebook to see examples of how to use qsymm.

Implemented algorithms

The two core concepts in qsymm are Hamiltonian families (Hamiltonians that may depend on free parameters) and symmetries. We provide powerful classes to handle these:

• Model is used to store symbolic Hamiltonians that may depend on momenta and other free parameters. We use sympy for symbolic manipulation, but our implementation utilizes numpy arrays for efficient calculations with matrix valued functions.

• PointGroupElement and ContinuousGroupGenerator are used to store symmetry operators. Besides the ability to combine symmetries, they can also be applied to a Model to transform it.

We implement algorithms that form a two-way connection between Hamiltonian families and symmetries.

• Symmetry finding is handled by symmetries, it takes a Model as input and finds all of its symmetries, including conserved quantities, time reversal, particle-hole, and spatial rotation symmetries. See symmetry_finder.ipynb and kekule.ipynb for detailed examples.

• continuum_hamiltonian and bloch_family are used to generate k.p or lattice Hamiltonians from symmetry constraints. See kdotp_generator.ipynb, bloch_generator.ipynb and kekule.ipynb for detailed examples.

Installation

qsymm works with Python 3.5 and is available on PyPI:

pip install qsymm

Some of the example notebooks also require Kwant.

Development

qsymm is on Gitlab, visit there if you would like to to contribute, report issues, or get the latest development version.