Toward extracting scattering phase shift from integrated correlation function

TL;DR

This work derives a relation linking integrated correlation functions of trapped two-particle systems to scattering phase shifts, offering an alternative method for phase shift extraction in lattice simulations at small Euclidean times.

Contribution

It introduces a novel relation connecting integrated correlation functions to scattering phase shifts, tested through perturbation theory and Monte Carlo simulations, providing a potentially more efficient extraction method.

Findings

The difference in integrated correlation functions converges rapidly to the infinite volume limit.

The proposed relation is validated through both perturbative calculations and Monte Carlo simulations.

It offers an alternative to the conventional large Euclidean time approach for phase shift extraction.

Abstract

In present work, a relation that connects the integrated correlation function of a trapped two-particle system to infinite volume particles scattering phase shift is derived. It has the potential to provide an alternative approach for extracting two-particle scattering phase shift from integrated correlation function in lattice simulation at small Euclidean time region. Both (i) perturbation calculation of 1+1 dimensional lattice Euclidean field theory model of fermions interacting with a contact interaction and (ii) Monte Carlo simulation of a 1D exactly solvable quantum mechanics model are carried out to test the proposed relation. In contrast to conventional two-step approach of extracting energy levels from temporal correlation function in lattice simulation at large Euclidean time first and then applying L\"uscher formula to convert energy levels into scattering phase shifts, we show that the difference of integrated correlation functions between interacting and noninteracting trapped systems converges rapidly to infinite volume limit that is given in terms of scattering phase shifts at small Euclidean time region.