Radius of convergence in lattice QCD at finite μB with rooted staggered fermions

Giordano, M. and Kapas, K. and Katz, S. D. and Nogradi, D. and Pásztor, Attila (2020) Radius of convergence in lattice QCD at finite μB with rooted staggered fermions. Physical Review D, 101 (7). No.-074511. ISSN 2470-0010

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Abstract

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity eμ/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 μ=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 show 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 Nt=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 μB/T≈2 and roughly temperature independent. Our simulations are performed at strange quark chemical potential μs=0, but the method can be straightforwardly extended to strangeness chemical potential μS=0 or strangeness neutrality.

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