Hubbard-Stratonovich-like Transformations for Few-Body Interactions

TL;DR

This paper introduces a new analytical framework for Hubbard-Stratonovich-like transformations that systematically include multi-body interactions, enhancing the accuracy of quantum many-body simulations involving three or more particles.

Contribution

It develops a systematic and controlled method to incorporate contact three- and multi-body interactions into Hubbard-Stratonovich transformations.

Findings

Framework enables inclusion of three-body forces in simulations.

Improves accuracy of many-body quantum calculations.

Facilitates systematic treatment of multi-body interactions.

Abstract

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the analytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three- and more-body interactions, is presented.