Many-body fits of phase-equivalent effective interactions

TL;DR

This paper develops a systematic method to control the off-shell behavior of phase-equivalent effective interactions in many-body systems, demonstrated through an application to trapped fermions at unitarity.

Contribution

It introduces a general approach for tuning off-shell properties of effective interactions to better match many-body system characteristics.

Findings

Method effectively adjusts off-shell behavior

Application improves modeling of trapped fermions at unitarity

Provides a systematic framework for many-body interaction renormalization

Abstract

In many-body theory it is often useful to renormalize short-distance, high-momentum components of an interaction via unitary transformations. Such transformations preserve the on-shell physical observables of the two-body system (mostly phase-shifts, hence unitarily-connected effective interactions are often called phase-equivalent), while modifying off-shell T-matrix elements influential in many-body systems. In this paper I lay out a general and systematic approach for controlling the off-shell behavior of an effective interaction, which can be adjusted to many-body properties, and present an application to trapped fermions at the unitary