Qcombo: A Python Package for Automated Commutator Calculations of Quantum Many-Body Operators

TL;DR

qcombo is a Python package that automates the symbolic calculation of commutators in quantum many-body operators, reducing errors and aiding the development of advanced many-body methods in physics and chemistry.

Contribution

It introduces an automated framework for commutator calculations in quantum many-body theory, specifically supporting the derivation of IMSRG flow equations.

Findings

Successfully automates the derivation of IMSRG flow equations.

Reduces human error in complex algebraic derivations.

Demonstrates application to multi-reference IMSRG at three-body truncation.

Abstract

qcombo is a Python package for the symbolic evaluation of commutators between general quantum many-body operators expressed in normal-ordered form using the generalized Wick theorem. The package provides an automated and systematic framework for generating the corresponding algebraic expressions, significantly reducing the risk of human error in lengthy and complex analytical derivations. It is designed to assist the development and implementation of modern many-body methods in nuclear physics, quantum chemistry, and related fields. The functionality and workflow of the package are demonstrated through an application to the in-medium similarity renormalization group (IMSRG) method, which has been widely used for nuclear ab initio calculations. As a representative example, qcombo is employed to automatically generate the complete set of multi-reference IMSRG flow equations with operators truncated at the normal-ordered three-body level.