New approach to canonical partition functions computation in 
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 lattice QCD at finite baryon density

Bornyakov, V. G.; Boyda, Denis; Goy, V. A.; Молочков, А. В.; Nakamura, Atsushi; Николаев, А. А.; Захаров, В. И.

doi:10.1103/physrevd.95.094506

Cited by 31 publications

(57 citation statements)

References 38 publications

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“…Notice that Roberge-Weiss symmetry [50] imposes that only coefficients of order 3n can be nonzero. The canonical partition functions are usually obtained as the coefficients of a Fourier expansion of the grandcanonical partition function at imaginary chemical potential [31,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]. Our direct determination from the eigenvalues of P is free from the systematic uncertainty associated with the extraction of Fourier coefficients from a discrete set of imaginary chemical potentials.…”

Section: A Generalitiesmentioning

confidence: 99%

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

et al. 2020

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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.

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Section: A Generalitiesmentioning

confidence: 99%

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

et al. 2020

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“…A similar formalism is also employed in the canonical approach [2][3][4][5], where the fugacity expansion is applied to the partition function Z itself (see Refs. [6,7] for recent developments).The net baryon density readswhere b k ðTÞ ≡ kp k ðTÞ. Analytic continuation to an imaginary chemical potential yields a purely imaginary ρ B =T 3 , with b k ðTÞ becoming its Fourier expansion coefficients.…”

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confidence: 99%

Cluster expansion model for QCD baryon number fluctuations: No phase transition at μB/T<π

et al. 2018

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A cluster expansion model (CEM), representing a relativistic extension of Mayer's cluster expansion, is constructed to study baryon number fluctuations in QCD. The temperature dependent first two coefficients, corresponding to the partial pressures in the baryon number B ¼ 1 and B ¼ 2 sectors, are the only model input, which we fix by recent lattice data at imaginary baryochemical potential. All other coefficients are constructed in terms of the first two and required to match the Stefan-Boltzmann limit of noninteracting quarks and gluons at T → ∞. The CEM allows calculations of the baryon number susceptibilities χ B k to arbitrary order. We obtain excellent agreement with all available lattice data for the baryon number fluctuation measures χ The grand canonical thermodynamic potential of QCD is an even function of the real baryon chemical potential μ B because of the CP-symmetry. Taking the quantization of the baryon charge into account, the QCD pressure has a fugacity expansionThis relation can formally be viewed as a relativistic extension of Mayer's cluster expansion in fugacities [1]. A similar formalism is also employed in the canonical approach [2][3][4][5], where the fugacity expansion is applied to the partition function Z itself (see Refs. [6,7] for recent developments).The net baryon density readswhere b k ðTÞ ≡ kp k ðTÞ. Analytic continuation to an imaginary chemical potential yields a purely imaginary ρ B =T 3 , with b k ðTÞ becoming its Fourier expansion coefficients. The analytic continuation to/from imaginary μ is one of the methods used to study QCD at finite net baryon density [8][9][10][11][12][13][14][15][16]. The leading four Fourier coefficients b k were studied in Refs. [17,18] using lattice simulations with physical quark masses at imaginary μ B , as well as phenomenological models.At low temperatures, below the crossover transition, a behavior similar to an uncorrelated gas of hadrons, i.e., jb k ðTÞ=b 1 ðTÞj ≪ 1 for k ≥ 2, is seen in lattice QCD (LQCD) [17,18]. Lattice simulations at T > 135 MeV yield negative b 2 ðTÞ values, which could be interpreted in terms of repulsive baryonic interactions. The first four LQCD Fourier coefficients, up to T ≃ 185 MeV, can indeed be described rather well by a hadron resonance gas (HRG) model with excluded-volume (EV) interactions between the (anti)

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“…The cluster expansion (2) of net baryon density is particularly interesting in the context of lattice QCD simulations at imaginary µ B . Indeed, ρ B attains a form of a trigonometric Fourier series for a purely imaginary µ B = i θ B T [12,17,18]. The cluster expansion coefficients b k become Fourier coefficients:…”

Section: Introductionmentioning

confidence: 99%

Critical point signatures in the cluster expansion in fugacities

et al. 2020

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The QCD baryon number density can formally be expanded into a Laurent series in fugacity, which is a relativistic generalization of Mayer's cluster expansion. We determine properties of the cluster expansion in a model with a phase transition and a critical point at finite baryon density, in which the Fourier coefficients of the expansion can be determined explicitly and to arbitrary order. The asymptotic behavior of Fourier coefficients changes qualitatively as one traverses the critical temperature and it is connected to the branching points of a thermodynamic potential associated with the phase transition. The results are discussed in the context of lattice QCD simulations at imaginary chemical potential. We argue that the location of a branching point closest to the imaginary chemical potential axis can be extracted through an analysis of an exponential suppression of Fourier coefficients. This is illustrated using the four leading coefficients both in a toy model as well as by using recent lattice QCD data.

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New approach to canonical partition functions computation in Nf=2 lattice QCD at finite baryon density

Cited by 31 publications

References 38 publications

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

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

Cluster expansion model for QCD baryon number fluctuations: No phase transition at μB/T<π

Critical point signatures in the cluster expansion in fugacities

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