Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice

Abstract

Without invoking any cumulant determination at the input level, we present here the first calculations of direct estimates of the Lee-Yang zeros of QCD partition function in (2+1)-flavor QCD. These zeros are obtained in complex isospin chemical potential ${\mu }_I$ plane using the unbiased exponential resummation formalism on $N_{\tau }=8$ lattices and with physical quark masses. For different temperatures, we illustrate the stability of the zeros closest to the origin from which, we subsequently procure the radius of convergence estimates. From the temperature-dependence study of the real and imaginary parts of these zeros, we try estimating one of the possible critical points forming the second order pion condensate critical line in the isospin phase diagram. Further, we compare these resummed estimates with the corresponding Mercer-Roberts estimates of the subsequent Taylor series expansions of the first three partition function cumulants. We also outline comparisons between resummed and Taylor series results of these cumulants for real and imaginary values of ${\mu }_I$ and highlight the behavior of different expansion orders within and beyond the obtained resummed estimates of radius of convergence. We also re-establish that this resummed radius of convergence can efficiently capture the onset of overlap problem for finite real ${\mu }_I$ simulations.

17 pages, 10 figures, comprehensive changes in title, abstract and main text, some new figures added and revised, present version matches with the journal version to be published in PRD

References in corpus (17)

• The equation of state in (2+1)-flavor QCD
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• The QCD crossover at finite chemical potential from lattice simulations
• The QCD phase structure at finite temperature and density
• Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at non-vanishing chemical potentials
• Second order cumulants of conserved charge fluctuations revisited I. Vanishing chemical potentials
• Towards finite density QCD with Taylor expansions
• Reliable estimation of the radius of convergence in finite density QCD
• Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density
• Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion
• Sign Problem in Quantum Monte Carlo Simulation
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
• Detecting critical points from Lee-Yang edge singularities in lattice QCD
• Searching for the QCD critical point using Lee-Yang edge singularities
• Color superconductivity on the lattice -- analytic predictions from QCD in a small box
• A new way of determining the Lattice QCD equation of state at a finite chemical potential

Cited by in corpus (1)

• Chiral symmetry breaking and pion condensation in the early universe