GTPack is a free Mathematica group theory package containing more than 200 modules developed for applications in condensed matter physics. We aim to achieve an optimal user experience by providing, e.g., a Mathematica-style documentation, an optional input validation, and guiding error messages and warnings.

GTPack builds a bridge between computational algebra, university education and modern research, with wide-ranging applications in condensed matter and solid-state physics, photonics, and quantum chemistry. The outline covers basic functionality, such as abstract group and representation theory, crystal and molecular structure tools and applications, e.g., electronic structure tools in the framework of crystal field theory or tight-binding.

GTPack allows for setting up and retrieving crystal and electronic structure databases (e.g. tight binding or crystal field parameters). Additionally, there is an ongoing effort to implement interfaces to investigate the output of standard software like ABINIT or VASP or the photonic band structure code MPB.

Latest version: GTPack 1.2 (June 2020)


Basic functionality: install point and space groups; calculate multiplication tables, classes, cosets, character tables, representation matrices, projection operators, Clebsch-Gordan coefficients, etc.

Structure: store, manipulate and generate structures of crystals and molecules; import/export to/from standard formats such as cif, POSCAR, etc.

Applications: construct Hamiltonians based on tight-binding, plane-wave expansion, crystal field theory; construct master equation for photonic crystals; calculate phonons based on harmonic approximation; analyze symmetry of electronic, photonic, phononic states; etc.

The application of GTPack is described with the book, Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica. Furthermore, we provide several tutorials to become familiar with the basic GTPack concepts.

More information on GTPack, including a complete command reference, can be found within our open access publication GTPack: A Mathematica group theory package for application in solid-state physics and photonics.

As an academic project, GTPack is designed for academic purposes and is free to use for anyone. To support the development of GTPack we ask you to cite two GTPack references as explained in Cite GTPack.