arXiv 2004.108002020-04hep-lat

有限密度下格点量子色动力学的新方法：粗格点上临界端点的结果

New approach to lattice QCD at finite density; results for the critical end point on coarse lattices

Matteo Giordano, Kornel Kapas, Sandor D. Katz, Daniel Nogradi, Attila Pasztor

备注：: 13 pages, 17 figures, references added
DOI：: 10.1007/JHEP05(2020)088

摘要：

目前用于研究有限重子密度格点量子色动力学的所有方法，除了众所周知的符号问题外，还存在不可控的系统不确定性。我们制定和测试的算法，符号重新加权，直接在有限的$μ= μ_B/3$，但没有任何这样的不受控制的系统。使用该算法，{ \em only}问题本身就是符号问题。这种方法涉及到生成配置的正费米子重量$|{\rm Re\; det} D(μ)|$其中$D(μ)$是狄拉克矩阵和符号${\rm sign} \; ( {\rm Re\; det} D(μ) ) = \pm 1$处理的离散重新加权。因此，只有两个扇区，$+1$和$-1$，并且只要平均值为$\langle\pm 1\rangle \neq 0$（相对于正权重），这种由符号进行的离散重新加权就没有重叠问题，并且结果是可靠的。在具有$2+1$味和物理夸克质量的$N_t = 4$格点上，采用未改进的交错离散方法对该方法进行了测试。通过测量空间晶格$L/a = 8, 10, 12$上裸耦合中的Fisher（有时也称为李-杨）零点，我们得出结论，在$μ= 0$处存在的交叉在$μ> 0$处变得更强，并且与$μ_B/T \sim 2.4$附近的真实相变一致。

英文摘要：

All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly at finite $μ= μ_B/3$ and is yet free from any such uncontrolled systematics. With this algorithm the {\em only} problem is the sign problem itself. This approach involves the generation of configurations with the positive fermionic weight $|{\rm Re\; det} D(μ)|$ where $D(μ)$ is the Dirac matrix and the signs ${\rm sign} \; ( {\rm Re\; det} D(μ) ) = \pm 1$ are handled by a discrete reweighting. Hence there are only two sectors, $+1$ and $-1$ and as long as the average $\langle\pm 1\rangle \neq 0$ (with respect to the positive weight) this discrete reweighting by the signs carries no overlap problem and the results are reliable. The approach is tested on $N_t = 4$ lattices with $2+1$ flavors and physical quark masses using the unimproved staggered discretization. By measuring the Fisher (sometimes also called Lee-Yang) zeros in the bare coupling on spatial lattices $L/a = 8, 10, 12$ we conclude that the cross-over present at $μ= 0$ becomes stronger at $μ> 0$ and is consistent with a true phase transition at around $μ_B/T \sim 2.4$.

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