Finite Density Simulations with Canonical Ensemble

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 .

Nuclear Physics A, 2009

The existence of the QCD critical point at non-zero baryon density is not only of great interest for experimental physics but also a challenge for the theory. Any hint of the existence of the first order phase transition and, particularly, its critical point will be valuable towards a full understanding of the QCD phase diagram. We use lattice simulation based on the canonical ensemble method to explore the finite baryon density and finite temperature region and look for the QCD critical point. As a benchmark, we run simulations for the four degenerate flavor QCD where we observe a clear signal of the expected first order phase transition. In the two flavor case, we do not see any signal for temperatures as low as 0.83 T c. Although our real world contains two light quarks and one heavier quark, three degenerate flavor case shares a lot of similar phase structures as the QCD. We scan the phase diagram using clover fermions with m π ≈ 700MeV on 6 3 × 4 lattices. The baryon chemical potential is measured as we increase the baryon number and we see the characteristic "S-shape" that signals the first order phase transition. We determine the phase boundaries by Maxwell construction and report our preliminary results for the location of critical point for the present lattice.

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.

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...

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

2005

We review a method for numerical simulations of lattice gauge theories at non-zero baryonic chemical potential we recently proposed. We first report on a test of the method using a solvable model and then present results for the phase structure of four flavour QCD. For the first time the region of chemical potential up to 1.4 T_C is explored, finding a first order transition line.

arXiv: High Energy Physics - Lattice, 2008

VICENTE AZCOITIDepartamento de Fisica Teorica, Universidad de ZaragozaPedro Cerbuna 12, E-50009 Zaragoza, SpainGIUSEPPE DI CARLOINFN, Laboratori Nazionali del Gran Sasso I-67010 Assergi (L’Aquila), ItalyANGELO GALANTEDipartimento di Fisica dell’ Universita’ di L’Aquila I-67100 L’Aquila, Italy andINFN, Laboratori Nazionali del Gran Sasso I-67010 Assergi (L’Aquila), ItalyVICTOR LALIENADepartamento de Fisica Teorica, Universidad de ZaragozaPedro Cerbuna 12, E-50009 Zaragoza, SpainWe review a method for numerical simulations of lattice gauge theories at non-zerobaryonic chemical potential we recently proposed. We first report on a test of the methodusing a solvable model and then present results for the phase structure of four flavourQCD. For the first time the region of chemical potential up to 1.4 T

We review a method for numerical simulations of lattice gauge theories at non-zero baryonic chemical potential we recently proposed. We first report on a test of the method using a solvable model and then present results for the phase structure of four flavour QCD. For the first time the region of chemical potential up to 1.4 T_C is explored, finding a first order transition line.

Physics Letters B, 1989

We present results of a numerical study of lattice QCD with four dynamical flavours of staggered fermions, performed by using a hybrid Monte Carlo algorithm on an 8× 123 lattice. We find a rapid change in the average value of the Polyakov loop at fie= 5.25 +_. 0.025 for a quark mass ma=0.025; at this mass value, the behaviour of the chiral order parameter, ( ~7~u), does not yet allow an independent determination of the transition point. Using existing hadron mass calculations, the value of Pc we have obtained here would lead to a transition temperature T~ 100 MeV.

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.