Extracting Resonance Width from Lattice Quantum Monte Carlo Simulations Using Analytical Continuation Method

TL;DR

This paper introduces a novel method combining lattice effective field theory and analytical continuation to directly extract nuclear resonance widths, overcoming previous limitations.

Contribution

It presents the first direct extraction of a nuclear resonance width within NLEFT using ACCC with a robust SVD-based Pade solver, demonstrating improved reliability.

Findings

Successfully extracted the $^5$He resonance energy and width.

Achieved results consistent with experimental data.

Developed a reliable numerical method for resonance analysis.

Abstract

Nuclear lattice effective field theory (NLEFT) provides an efficient ab initio framework for computing low-lying states via imaginary-time projection. However, the extraction of unstable resonances, especially those with broad widths, remains a significant challenge. Traditional techniques such as the complex scaling method are often limited by sign problems or inherent statistical uncertainties. In this work, we present the first direct extraction of a nuclear resonance width within NLEFT by combining a high-precision, sign-problem-free nuclear interaction with the analytical continuation in the coupling constant (ACCC) approach. To address numerical instabilities in the ACCC framework, we implement a robust Pade solver based on singular value decomposition (SVD), incorporating ridge regularization and pole-safety criteria to ensure reliable extrapolation to the resonance pole. We detail the methodology and apply it to the unbound ground state of $^5$He ($J^\pi=3/2^-$). Our calculation yields a resonance energy $E=0.80(10)$ MeV and a width $\Gamma=1.05(9)$ MeV, in agreement with recent experimental results ($E_{\rm exp}=0.798$ MeV, $\Gamma_{\rm exp}=0.648$ MeV). This work establishes a practical and precise strategy for studying resonances within the ab initio lattice framework, paving the way for investigations of many-body resonances in exotic nuclei near the drip lines.