Canonical approach to finite density QCD with multiple precision computation

Fukuda, Ryoichi; Nakamura, Atsushi; Oka, Shotaro

doi:10.1103/physrevd.93.094508

Cited by 18 publications

(18 citation statements)

References 25 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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“…Although the difficulty associated with the complex fermion determinant remains as the highly oscillating integral, authors of Refs. [4][5][6] pointed out that the integral can be carried out with a multi-precision arithmetic. Once the canonical partition functions are extracted, the grand canonical partition function Z GC (µ q , T, V ) with an arbitrary chemical potential can be constructed via the fugacity expansion,…”

Section: Introductionmentioning

confidence: 99%

Lee-Yang zeros in lattice QCD for searching phase transition points

et al. 2019

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We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, n , are calculated at the pure imaginary chemical potential iµ qI , where no sign problem occurs. Then, the canonical partition functions, Z C (n, T, V ), up to some maximal values of n are estimated through fitting theoretically motivated functions to n , which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T /T c = 0.84 -1.35.In the distributions of the Lee-Yang zeros, we observe the Roberge-Weiss phase transition at T /T c ≥ 1.20. We discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n, so that we can estimate a reliable infinite volume limit.

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“…We summarize what has been achieved in this paper to explore the QCD phase diagram: using the simple fugacity expansion formula derived from the hopping parameter expansion, combined with the multi-precision numerical calculation [36], we evaluate the canonical partition functions up to the large quark number. This allows us to calculate high-density region, i.e., µ/T > 1.…”

Section: Resultsmentioning

confidence: 99%

“…The numerical Fourier transformation can be executed safely by using the multiple precision calculation [36] without any sign problem. This is because the fugacity dependence of the determinant or the partition function is given analytically once we evaluate the fugacity expansion coefficient w n .…”

Section: Jhep02(2016)054mentioning

confidence: 99%

QCD phase transition at real chemical potential with canonical approach

Nakamura

Oka

Taniguchi

2016

J. High Energ. Phys.

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We study the finite density phase transition in the lattice QCD at real chemical potential. We adopt a canonical approach and the canonical partition function is constructed for N f = 2 QCD. After derivation of the canonical partition function we calculate observables like the pressure, the quark number density, its second cumulant and the chiral condensate as a function of the real chemical potential. We covered a wide range of temperature region starting from the confining low to the deconfining high temperature; 0.65T c ≤ T ≤ 3.62T c . We observe a possible signal of the deconfinement and the chiral restoration phase transition at real chemical potential below T c starting from the confining phase. We give also the convergence range of the fugacity expansion.

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Canonical approach to finite density QCD with multiple precision computation

Cited by 18 publications

References 25 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

Lee-Yang zeros in lattice QCD for searching phase transition points

QCD phase transition at real chemical potential with canonical approach

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