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 $T_c$.
Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach
本文将回顾基于有限化学势的格点量子色动力学的有限密度算法，并总结其中的难点。我将提出一个正则系综方法，它从费米子行列式中投影出有限重子数扇区。对于这个算法的工作，它需要一个有效的方法来计算费米子行列式和蒙特卡罗算法，它容纳无偏估计的概率。我将报告沿这一方向取得的进展与Padé - Z $_2$估计的行列式及其实施的新开发的噪声蒙特卡罗算法。
