Complex Langevin for Lattice QCD
Complex Langevin for Lattice QCD
复制标题
格子 QCD 的复朗之万
DOI：
--
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
J. Kogut
中科院分区：
文献类型：
--
作者：
D. Sinclair;J. Kogut
我们用规范冷却和自适应更新的复朗之万方程(CLE)模拟了有限夸克数化学势下的晶格QCD，以防止不稳定性。使用CLE是因为有限元的QCD有一个复杂的费米子行列式，这排除了基于重要性抽样的标准模拟方法的使用。由于即使当CLE模拟收敛时，它们也不能保证产生正确的结果，除非在非常严格的条件下，这是有限格子QCD不遵守的，所以我们需要广泛的测试来确定它在什么条件下产生可靠的结果。我们在$\beta=6/g^2=5.6$和$\beta=5.7$时进行了模拟，两者都是$m=0.025$。对于足够大到足以产生饱和的小的$\MU$和$\MU$，随着耦合的减小，测量的观测值似乎正在接近它们的正确值。然而，对于中间的$\Mu$值，这些模拟预测从强子物质到核物质的转变$\Mu$太小了。由于有证据表明，为了使CLE模拟产生正确的结果，轨迹应该保持在$SU(3)$流形附近(至少对于小的$\MU$)，我们探索参数空间以查看哪里是正确的。我们发现，到这个流形的距离随着耦合的减小和夸克质量(以晶格为单位)的减小而减小，即当我们接近连续介质极限时。这表明，我们需要在较小的耦合和夸克质量(需要更大的晶格)下进行模拟，看看它们是否能产生正确的物理。
We simulate lattice QCD at finite quark-number chemical potential, $\mu$, using the complex-Langevin equation (CLE) with gauge-cooling and adaptive updating to prevent instabilities. The CLE is used because QCD at finite $\mu$ has a complex fermion determinant which precludes the use of standard simulation methods based on importance sampling. Since, even when CLE simulations converge, they are not guaranteed to produce correct results except under very stringent conditions, which lattice QCD at finite $\mu$ does not obey, we need extensive testing to determine under what conditions it produces reliable results. We performed simulations at $\beta=6/g^2=5.6$ and $\beta=5.7$, both at $m=0.025$. For small $\mu$ and $\mu$ large enough to produce saturation, measured observables appear to be approaching their correct values as the coupling is decreased. However, for intermediate $\mu$ values, these simulations predict a transition from hadronic to nuclear matter at a $\mu$ which is far too small. Since there is evidence that for CLE simulations to produce correct results the trajectories should remain close to the $SU(3)$ manifold (at least for small $\mu$), we explore the parameter space to see where this is true. We find that the distance from this manifold decreases as the coupling decreases and as the quark mass (in lattice units) decreases, i.e. as we approach the continuum limit. This indicates that we need to simulate at smaller couplings and quark masses (requiring larger lattices) to see if these can produce the correct physics.
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影响因子：
5
作者：
Z. Fodor;Z. Fodor;S. Katz;D. Sexty;C. Torok
通讯作者：
Z. Fodor;Z. Fodor;S. Katz;D. Sexty;C. Torok
DOI：
10.1051/epjconf/201817501019
发表时间：
2017-08
期刊：
--
影响因子：
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作者：
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通讯作者：
E. Seiler
影响因子：
2.7
作者：
Aarts, Gert;Bongiovanni, Lorenzo;Stamatescu, Ion-Olimpiu
通讯作者：
Stamatescu, Ion-Olimpiu
影响因子：
5
作者：
G. Aarts;E. Seiler;I. Stamatescu
通讯作者：
G. Aarts;E. Seiler;I. Stamatescu