SNEG - Mathematica package for symbolic calculations with second-quantization-operator expressions

TL;DR

The paper introduces SNEG, a Mathematica package that facilitates symbolic calculations with second-quantization operators, enabling flexible and efficient manipulation of operator expressions in many-particle physics problems.

Contribution

It presents a new Mathematica package that translates between various representations of second-quantization operators, enhancing symbolic manipulation and computational efficiency.

Findings

Supports multiple notation formats for operators

Includes a comprehensive library of transformation rules

Can be adapted for various physics problems involving non-commuting operators

Abstract

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears advantageous to write numerical computer codes which allow the user to define the problem and the quantities of interest directly in terms of operator strings, rather than in some low-level programming language. Here I describe a Mathematica package which provides a flexible framework for performing the required translations between several different representations of operator expressions: condensed notation using pure ASCII character strings, traditional notation ("pretty printing"), internal Mathematica representation using nested lists (used for automatic symbolic manipulations), and various higher-level ("macro") expressions. The package consists of a collection of transformation rules that define the algebra of operators and a comprehensive library of utility functions. While the emphasis is given on the problems from solid-state and atomic physics, the package can be easily adapted to any given problem involving non-commuting operators. It can be used for educational and demonstration purposes, but also for direct calculations of problems of moderate size.