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

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 (Padé) 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.

9 pages 6 figures and 2 tables. Talk at 38th international Lattice conference 2021 online Zoom/Gather @ MIT, USA

References in corpus (7)

• QCD at finite chemical potential with six time slices
• Apparent convergence of Padé approximants for the crossover line in finite density QCD
• Mapping the phase diagram of strongly interacting matter
• Net-baryon number fluctuations
• Taylor expansions on Lefschetz thimbles (and not only that)
• Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD
• Universality, Lee-Yang singularities and series expansions