Radius of convergence in lattice QCD at finite ${\mu }_B$ with rooted staggered fermions

Abstract

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $e^{\mu /T}$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $\mu =0$. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We argue that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. This is a cutoff effect that potentially affects all estimates of the radius of convergence with the standard staggered rooting. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial, and, therefore of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at $N_t=4$. We perform a finite-volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be ${\mu }_B/T\approx 2$ and roughly temperature independent. Our simulations are performed at strange quark chemical potential ${\mu }_s=0$, but the method can be straightforwardly extended to strangeness chemical potential ${\mu }_S=0$ or strangeness neutrality.

12 pages, 11 figures; v2: contains corrections to the formulas from the erratum PRD 104, 119901(E) (2021); results unchanged

References in corpus (21)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD transition temperature: results with physical masses in the continuum limit
• The QCD transition temperature: results with physical masses in the continuum limit II.
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• QCD at finite chemical potential with six time slices
• Canonical partition function and finite density phase transition in lattice QCD
• Finite density QCD with a canonical approach
• Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential
• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• On the critical line of 2+1 flavor QCD
• Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method
• Breakdown of staggered fermions at nonzero chemical potential
• Reliable estimation of the radius of convergence in finite density QCD
• QCD at non-zero density and canonical partition functions with Wilson fermions
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• Winding expansion techniques for lattice QCD with chemical potential
• Mapping the phase diagram of strongly interacting matter
• Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD
• Polyakov loops and spectral properties of the staggered Dirac operator
• Generalized quark number susceptibilities from fugacity expansion at finite chemical potential for $N_f$ = 2 Wilson fermions
• Hadron spectroscopy from canonical partition functions

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• Hydrodynamic description of the baryon-charged quark-gluon plasma
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