Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method

TL;DR

This paper investigates the finite density phase transition in lattice QCD with 2 and 4 flavors using a canonical ensemble approach, developing a winding number expansion method to identify the critical point and phase boundaries.

Contribution

It introduces a winding number expansion method for accurate particle number projection, enabling the study of phase transitions in lattice QCD at finite density.

Findings

Observed first order phase transition signals for Nf=4 via S-shape in chemical potential-density plane.

Determined phase boundaries and critical point consistent with theoretical expectations.

Did not find a mixed phase signal for Nf=2 at temperatures as low as 0.83 Tc.

Abstract

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 $\mu = 0$. 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 $T_c$.