Numerical study of the Roberge-Weiss transition

Physical Review D, 2015

Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. We present analytic derivation of the canonical partition functions and Lee-Yang zeros based on the free energy in the Stefan-Boltzmann limit using a saddle point approximation. We also perform lattice QCD simulation in a canonical approach using the fugacity expansion of the fermion determinant, and carefully examine its reliability. By comparing the analytic and numerical results, we conclude that the canonical partition functions follow the Gaussian distribution of the baryon number, and the accumulation of Lee-Yang zeros of these canonical partition functions exhibit the first order Roberge-Weiss phase transition. We discuss the validity and applicable range of the result, and its implications both for theoretical and experimental studies.

Physics Letters B

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.

arXiv: High Energy Physics - Lattice, 2018

We report Lee-Yang zeros behavior at finite temperature and density using the canonical approach in lattice QCD. The quark number densities are calculated at the pure imaginary chemical potential in lattice QCD. Canonical partition functions Z_C(n,T,V) up to some maximal values of n are obtained through fitting the theoretically motivated functions to the quark number densities and 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. A Roberge-Weiss phase transition at T/T_c > 1.20 is observed in the distributions of the Lee-Yang zeros. We also discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n.

Journal of High Energy Physics, 2016

We study the finite density phase transition in the lattice QCD at real chemical potential. We adopt 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. We observe signals for the deconfinement and the chiral restoration phase transition at real chemical potential below T c starting from the confining phase.

Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012)

arXiv (Cornell University), 2021

We study lattice two-color QCD (QC2D) with two flavors of staggered fermions at imaginary and real quark chemical potential µq and T > Tc. We employ various methods of analytic continuation of the quark number density from imaginary to real quark chemical potentials µq, including series expansions as well as based on phenomenological models, and study their accuracy by comparing the results to the lattice data. Below the Roberge-Weiss temperature, T < TRW , we find that the cluster expansion model provides an accurate analytic continuation of the baryon number density in the studied range of chemical potentials. On the other hand, the behavior of the reconstructed canonical partition functions indicate that the available models may require corrections at high quark densities. At T > TRW we show that the analytic continuation to the real values of µq based on trigonometric functions works equally well with the conventional method based on the Taylor expansion in powers of µq.

Physical Review D, 2022

We present a calculation of the net baryon number density as a function of imaginary baryon number chemical potential, obtained with highly improved staggered quarks at temporal lattice extent of Nτ = 4, 6. We construct various rational function approximations of the lattice data and discuss how poles in the complex plane can be determined from them. We compare our results of the singularities in the chemical potential plane to the theoretically expected positions of the Lee-Yang edge singularity in the vicinity of the Roberge-Weiss and chiral phase transitions. We find a temperature scaling that is in accordance with the expected power law behavior.

Nuclear Physics A, 1998

The Grand Canonical formalism is generally used in numerical simulations of finite density QCD since it allows free mobility in the chemical potential µ. We show that special care has to be used in extracting numerical results to avoid dramatic rounding effects and spurious transition signals. If we analyze data correctly, with reasonable statistics, no signal of first order phase transition is present and results using the Glasgow prescription are practically coincident with the ones obtained using the modulus of the fermionic determinant.

Nuclear Physics B, 1990

A method proposed by Barbour, Davies and Sabeur is used to expand the grand canonical partition function for QCD on a finite lattice in terms of the canonical partition functions for a fixed number of fermions. We show how the lattice action corresponding to the canonical partition function for a given fermion number can be obtained. The method is not unique to QCD and can be applied to other theories with complex action. This expansion of the GCPF is used to study QCD at finite density. The results of preliminary numerical simulations performed on a 44 lattice are described. Evidence is found for the positivity and continuity of the canonical partition functions as a function of the fermion number. The number density shows a clear signal of a transition at a density (in lattice units) of about 0.35 at /3 = 4.9 and small quark mass.

EPJ Web of Conferences

The canonical approach is a powerful tool to circumvent sign problem in LQCD. Although it has its own difficulties it provides opportunity to determine QCD phase transition line. Using improved Wilson fermions we calculated number density at nonzero imaginary chemical potential for confinement and deconfinement phases, restored canonical partition functions Zn and did extrapolation into the real chemical potential region. We computed the higher moments of the baryon number including the kurtosis, and compared our results with information from relativistic heavy ion collision experiments.