wickop: Lattice Cubic Rotation Operator Generator

TL;DR

The paper presents wickop, a Python 2.7 tool for generating lattice cubic rotation operators by efficiently computing tensor products of symmetry-adapted building blocks, handling any momentum representation.

Contribution

Introduction of wickop, a Python tool that automates the creation of symmetry-adapted operators for lattice cubic groups, including momentum-dependent representations.

Findings

Efficient operator generation using tensor products and character tables.

Handles arbitrary momentum representations with little group classification.

Ensures consistent basis construction for operators in lattice simulations.

Abstract

This document outlines the usage of a series of python 2.7 scripts designed to easily and efficiently create compound operators. This is accomplished by computing tensor products of smaller building blocks that transform irreducibly under lattice cubic rotational and translational symmetry. In particular, the code has the ability to handle representations of the cubic rotation group with any spatial momentum. The key paradigm is to track the momentum separately from the rotations, fully utilizing the abelian structure of the translation subgroup. This goes through the Wigner little group method to classify the subgroup of rotations that leave the momentum direction unchanged. Using little groups circumvents the issue of a volume factor in the number of representation matrices that are needed, instead only requiring the 96 cubic rotation representation matrices. Tensor products are computed with character tables and Clebsch-Gordan coefficients are saved for each decomposition in the tensor product. The code also builds operators in a consistent basis, ensuring that operators that transform in the same representation have the same properties.