Towards extremely dense matter on the lattice, XQCD-J Collaboration
Towards extremely dense matter on the lattice, XQCD-J Collaboration
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针对晶格上极其致密的物质，XQCD-J 合作
DOI：
10.1093/ptep/pts003
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A.Nakamura et al.
中科院分区：
文献类型：
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作者：
福田努;A.Nakamura et al.
量子色动力学（QCD）有望具有丰富的相结构。根据经验，在晶格 QCD 模拟中很难获得低温和非零化学势 μ 区域。我们通过使用费米子行列式的降维公式来解决晶格 QCD 中的这个问题。我们研究了约简公式的约简矩阵的光谱特性。不同晶格尺寸的晶格模拟表明，简化矩阵的特征值遵循时间大小 Nt 的缩放定律。使用还原公式检查费米子行列式的性质。我们发现，由于 Nt 缩放定律，随着 T 的减小，费米子行列式变得对 μ 不敏感，并且在 T=0 时 μ<mπ/2 时与 μ 无关。 Nt 标度定律为费米子行列式提供了两种类型的低温极限：(i) 一种用于低密度，(ii) 一种用于高密度。在这两种情况下，费米子行列式都成为真实的，并且理论不受符号问题的影响。在 (ii) 的情况下，QCD 接近一种理论，其中夸克仅在空间方向上相互作用，而胶子通过普通的杨-米尔斯作用相互作用。即使存在动力夸克，由于不存在夸克的时间相互作用，配分函数也变得完全 Z3 不变。约简公式也适用于规范形式主义和李杨零定理。我们发现了正则分布和李-杨零轨迹的特征温度依赖性。使用正则配分函数的假设，我们讨论了这些温度依赖性的物理意义，并表明正则分布和 Lee-Yang 零轨迹的变化与 μ 诱导相变的存在/不存在有关。
Quantum chromodynamics (QCD) is expected to have a rich phase structure. It is empirically known to be difficult to access low-temperature and nonzero chemical potentialμregions in lattice QCD simulations. We address this issue in lattice QCD with the use of a dimensional reduction formula for the fermion determinant. We investigate the spectral properties of a reduced matrix of the reduction formula. Lattice simulations with different lattice sizes show that the eigenvalues of the reduced matrix follow a scaling law for the temporal sizeNt. The properties of the fermion determinant are examined using the reduction formula. We find that, as a consequence of theNt-scaling law, the fermion determinant becomes insensitive toμasTdecreases, and isμ-independent atT=0 forμ<mπ/2. TheNt-scaling law provides two types of low-temperature limit for the fermion determinant: (i) one for low density and (ii) one for high density. The fermion determinant becomes real and the theory is free from the sign problem in both cases. In the case of (ii), QCD approaches a theory in which quarks only interact in spatial directions, and gluons interact via the ordinary Yang–Mills action. The partition function becomes exactlyZ3invariant even in the presence of dynamical quarks because of the absence of the temporal interaction of quarks. The reduction formula is also applied to the canonical formalism and the Lee–Yang zero theorem. We find characteristic temperature dependences for the canonical distribution and the Lee–Yang zero trajectory. Using an assumption on the canonical partition function, we discuss the physical meaning of these temperature dependences and show that the changes in the canonical distribution and Lee–Yang zero trajectory are related to the existence/absence ofμ-induced phase transitions.