Hamilton Operators, Discrete Symmetries, Brute Force and SymbolicC++

TL;DR

This paper presents a brute force computational method to identify discrete symmetries of Hamilton operators in finite-dimensional quantum systems, with implementations for spin and Fermi systems using SymbolicC++.

Contribution

It introduces a novel brute force approach and provides a SymbolicC++ implementation for finding permutation matrix symmetries of Hamilton operators.

Findings

Successfully identifies discrete symmetries in example systems

Provides a practical computational tool for symmetry analysis

Demonstrates applicability to spin and Fermi systems

Abstract

To find the discrete symmetries of a Hamilton operator $\hat H$ is of central importance in quantum theory. Here we describe and implement a brute force method to determine the discrete symmetries given by permutation matrices for Hamilton operators acting in a finite-dimensional Hilbert space. Spin and Fermi systems are considered as examples. A computer algebra implementation in SymbolicC++ is provided.