arXiv 1609.045502016-09hep-th

强耦合区域熵的理论性质

Theoretical Properties of Entropy in a Strong Coupling Region

Chen-Te Ma

备注：: 29 pages, major changes, references added

摘要：

熵是计算系统中物理自由度的量。在有限温度下，人们可以用热熵来研究材料的物理性质。在零温度下，纠缠熵有望提供一个合适的相结构的序参量。特别是在强耦合共形场论中，纠缠熵呈现出一个有趣的余维二面积定律。我们从一个精确的有效势出发，计算了费米子质量无限大的非相对论模型中的热熵，得到了无限强耦合极限下的热熵。计算结果表明，在有限晶格间距下，在无限强耦合极限下，热熵为零。在强耦合格点系统中引入非平凡拓扑项，得到非平凡熵，并由非平凡熵标记系统的拓扑。我们首先计算了二维格点拓扑量子场论的热熵来研究格点伪影，并论证了如果系统在纠缠熵中不存在体积定律，则理论可能具有平移不变性。最后，我们证明了在二维共形场论中，对于一个区间情形，纠缠熵的普适项的系数不受纠缠面的选择的影响.讨论了在大$N$极限下二维$\mathrm{CP}^{N-1}$模型中纠缠熵的纠缠面选择问题。

英文摘要：

Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a suitable order parameter of a phase structure. Especially, the entanglement entropy exhibits an interesting codimension two area law in a strongly coupled conformal field theory. We compute thermal entropy in a non-relativistic model with an infinite fermion mass limit from an exact effective potential to obtain thermal entropy at an infinite strong coupling limit. The computational result provides vanishing thermal entropy at an infinite strong coupling limit with a finite lattice spacing. The non-trivial topological term can be included in the strongly coupled lattice system to obtain the non-trivial entropy and the topology can be marked from the entropy. We first compute the thermal entropy in a two dimensional lattice topological quantum field theory to study the lattice artifact and also argue that a theory possibly has translational invariance if a system does not have a volume law in the entanglement entropy. Finally, we show that a coefficient of a universal term of the entanglement entropy should not be affected by a choice of an entangling surface in two dimensional conformal field theory for one interval case. We also discuss a choice of the entangling surface in the entanglement entropy in two dimensional $\mathrm{CP}^{N-1}$ model at the large $N$ limit.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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