Detecting critical points from Lee-Yang edge singularities in lattice QCD

TL;DR

This paper introduces a novel method combining Taylor expansion and Padé approximants to analyze Lee-Yang edge singularities in lattice QCD, providing insights into the phase structure at complex chemical potentials.

Contribution

It presents a new approach using rational approximants to study singularities in lattice QCD, enhancing understanding of phase transitions at complex chemical potentials.

Findings

Identified the position of Lee-Yang edge singularities in lattice QCD data.

Observed scaling behavior consistent with the Roberge-Weiss transition at high temperatures.

Detected different singularity behaviors below approximately 170 MeV.

Abstract

A new approach is presented to explore the singularity structure of lattice QCD in the complex chemical potential plane. 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. We present a calculation of the cumulants of the net-baryon number as a function of a purely imaginary baryon number chemical potential, obtained with highly improved staggered quarks at temporal lattice extent of $N_\tau=4,6$. We construct various rational function approximations of the lattice data and determine their poles (and roots) in the complex plane. We compare the position of the closest pole to the theoretically expected position of the Lee-Yang edge singularity. At high temperature, we find scaling that is in accordance with the expected power law behavior of the Roberge-Weiss transition while a different behavior is found for $T\lesssim 170$ MeV.