Phase transition(s) in finite density QCD

2018

The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This is why, we can not calculate physical quantities accurately at finite chemical potential. In this study, we try to beat the sign problem using canonical approach of finite density lattice QCD. Although it is known that the canonical approach has several numerical problems, we can reduce them and calculate thermodynamic observables accurately at finite density. In this thesis, we will see how to improve the canonical approach and a result of thermodynamic observables which are related to the QCD phase transition at finite density. Our study focused on baryon number susceptibility. A peak in baryon number susceptibility corresponds to the confinement--deconfinement phase transition. In this study, we do not see the QCD phase transition yet. However...

Physics Letters B, 1998

We report results of simulations of strong coupling, finite density QCD obtained within a MFA inspired approach where the fermion determinant in the integration measure is replaced by its absolute value. Contrary to the standard wisdom, we show that within this approach a clear signal for a first order phase transition appears with a critical chemical potential in extremely good agreement with the results obtained with the Glasgow algorithm. The modulus of the fermion determinant seems therefore to preserve some of the relevant physical properties of the system. We also analyze the dependence of our results on the quark mass, including both the chiral and large mass limit, and the theory in the quenched approximation.

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.

Physical Review D, 2010

In a progress toward searching for the QCD critical point, we study the finite density phase transition of N f = 4 and 2 lattice QCD at finite temperature with the canonical ensemble approach. We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon chemical potential from the canonical approach to look for the mixed phase as a signal for the first order phase transition. In the case of N f = 4, we observe an "S-shape" structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below T c. The intersecting point of the two extrapolated boundaries turns out to be at the expected first order transition point at T c with µ = 0. This serves as a check for our method of identifying the critical point. We also studied the N f = 2 case, but do not see a signal of the mixed phase for temperature as low as 0.83 T c .

2007

We present some new results regarding simulations of nite density QCD based on a canonical approach. A previous study has shown that such simulations are feasible, at least on small lattices. In the current study, we investigate some of the issues left open: we study the errors introduced by our approximation of the action and we show how to tune it to reduce the cost of the simulations while keeping the errors under control. To further reduce the cost of the simulations, we check the reliability of reweighting method with respect to the baryon number. Finally, using these optimizations, we carry out the simulations at larger densities than in our previous study to look for signals of a phase transition.

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.

Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

In this lecture we discuss various properties of the phase factor of the fermion determinant for QCD at nonzero chemical potential. Its effect on physical observables is elucidated by comparing the phase diagram of QCD and phase quenched QCD and by illustrating the failure of the Banks-Casher formula with the example of one-dimensional QCD. The average phase factor and the distribution of the phase are calculated to one-loop order in chiral perturbation theory. In quantitative agreement with lattice QCD results, we find that the distribution is Gaussian with a width ∼ µT √ V (for m π ≪ T ≪ Λ QCD). Finally, we introduce, so-called teflon plated observables which can be calculated accurately by Monte Carlo even though the sign problem is severe.

Nuclear Physics B, 1990

Numerical results are presented for lattice QCD with m = 0.1 four-flavour staggered fermions around the finite-temperature transition at /3 5.13 on a i0 3 x 4 volume using the Hybrid Monte Carlo. A method is described that extends the /3 range that can be analysed using data gathered at only one /3 value. The nature of the order of the transition at m 0.1 is discussed using results from 6~x 4-10~x 4 volumes. Over this range, a standard test indicates that the data are more consistent with a sharp crossover and shows that the first-order transition, when it develops on larger lattices, must be rather weak.

EPJ Web of Conferences, 2017

At finite baryon density lattice QCD first-principle calculations can not be performed due to the sign problem. In order to circumvent this problem, we use the canonical approach, which provides reliable analytical continuation from the imaginary chemical potential region to the real chemical potential region. We briefly present the canonical partition function method, describe our formulation, and show the results, obtained for two temperatures: T/T c = 0.93 and T/T c = 0.99 in lattice QCD with two flavors of improved Wilson fermions.

Journal of High Energy Physics, 2004

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, test it in the Gross-Neveu model at finite baryon density, and apply it to the study of the chemical potential-temperature phase diagram of QCD with four degenerate flavors of Kogut-Susskind type.