Radius of convergence in lattice QCD at finite μB 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 µ 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. 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 at µ B T ≈ 2 and roughly temperature independent.

Effect of stout smearing on the phase diagram from multiparameter reweighting in lattice QCD

“…As a side analysis, we have compared the Fisher zeros obtained using the recently introduced geometric matching method [44], with those obtained with the standard rooting. While the two methods are expected to lead to the same continuum limit, finite lattice spacing effects could be very different.…”

“…where P stands for "paried" and the set of the ξ i are obtained from the set of the λ i via geometric matching [44]. Essentially, they are the geometric means of the close-lying pairs of λ i .…”

Overview of the QCD phase diagram

“…For this case, Ref. [ 87 ] introduces a new definition of the rooted staggered determinant, which allows for a numerical study of the Lee–Yang zeros. It is then tested on an lattice with stout smeared staggered fermions and a Symanzik improved gauge action.…”

“…In Ref. [ 88 ], an algorithm called sign-reweighting is proposed, aiming to avoid uncontrolled systematics like the overlap problem. This approach separates the sign of the Dirac determinant from the configuration generation which is done with a weight of .…”

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

“…They could thereby explain the nonanalytic behavior of the free energy that develops in the thermodynamic limit and signals a phase transition. The Lee-Yang formalism has been applied to a variety of equilibrium problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and it has been realized that the framework can also be used to understand nonequilibrium phase transitions [19][20][21][22][23][24], such as dynamical phase transitions in quantum systems after a quench [25][26][27] and space-time phase transitions in glass formers [28][29][30][31] and open quantum systems [32][33][34].…”