Lee-Yang edge singularities in lattice QCD : A systematic study of singularities in the complex $\mu_B$ plane using rational approximations

TL;DR

This paper introduces a novel method combining Taylor expansion and rational approximants to identify singularities in lattice QCD at imaginary chemical potential, focusing on the complex plane of baryon chemical potential.

Contribution

It presents a new approach using Padé approximants to study Lee-Yang edge singularities in lattice QCD, validated through numerical experiments on toy models and applied to 2+1 flavor QCD.

Findings

Detected signatures of Roberge-Weiss critical point

Identified chiral singularities with some caveats

Validated method with toy model experiments

Abstract

A new approach is presented to explore the singularity structure of lattice QCD at imaginary chemical potential. Our method can be seen as a combination of the Taylor expansion and analytic continuation approaches. Its novelty lies in using rational (Pad\'e) approximants for studying Lee Yang edge singularities. The motivation for using rational approximants will be exhibited. We will provide some confidence in our approach based on numerical experiments performed on well-motivated "toy models". Our focus lies in identifying singularities of the net-baryon number density in the complex $\mu_B$ plane. To this end we have found signatures of the Roberge-Weiss critical point(and Chiral singularities -- subject to some caveats). In this contribution we will discuss the setup, simulation parameters and results obtained for 2+1 flavor QCD in the complex $\mu_B/T$ plane.