论文标题
QCD中的复杂兰格文计算有限密度
Complex Langevin calculations in QCD at finite density
论文作者
论文摘要
我们证明，复杂的langevin方法（CLM）可以在有限密度的参数状态下启用QCD的计算，在该参数状态下，由于严重的符号问题，常规方法（例如状态方法的密度和泰勒膨胀方法）不适用于QCD。在这里，我们使用$β= 5.7 $的PLAQUETTE量规动作，并使用简介的Quark Mass $ M A = 0.01 $和非零夸克化学势$μ$。我们确认，在$ 8^3 \ times 16 $ lattice和$ 16^32 $ 32 $ lattice上，满足了$ 8^3 \ times 16 $ lattice的$μ/t = 5.2-7.2 $的足够条件。特别是，发现夸克数的期望值相对于$μ$具有平稳性，两个晶格的高度为24。可以从夸克的费米分布中理解这个高原，其高度与单个夸克的自由度相吻合，其动量为零，即3（颜色）$ \ times $ 4（味道）$ \ times $ \ times $ 2（spin）$ = 24 $。我们的结果可能被视为迈向费米球体形成的第一步，费米球体在有效理论的颜色超导性中起着至关重要的作用。
We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $β= 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $μ$. We confirm that a sufficient condition for correct convergence is satisfied for $μ/T = 5.2 - 7.2$ on a $8^3 \times 16$ lattice and $μ/T = 1.6 - 9.6$ on a $16^3 \times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $μ$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $\times$ 4 (flavor) $\times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.
