Counting Rules of Nambu–Goldstone Modes
Counting Rules of Nambu–Goldstone Modes
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DOI：
10.1146/annurev-conmatphys-031119-050644
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发表时间：
2019-04
影响因子：
22.6
通讯作者：
Haruki Watanabe
中科院分区：
文献类型：
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作者：
Haruki Watanabe
当整体连续对称性自发破缺时，会出现无间隙的集体激发，称为Nambu-Goldstone模（NGM），它控制着系统的低能性质。这一著名定理的应用范围从高能粒子物理到凝聚态和原子物理。当对称性破缺发生在缺乏洛伦兹不变性的系统中时，如通常在凝聚态系统中的情况，所产生的NGM的数量可以低于破缺对称性生成器的数量，并且NGM的色散不一定是线性的。在这篇文章中，我们回顾了最近建立的公式NGM与破碎的内部对称性，同样适用于相对论和非相对论系统。我们还讨论了NGM起源于时空对称性破缺的复杂性。沿着，我们涵盖了许多启发性的例子，从不同的背景。我们还提出了一个补充的观点，从Lieb-Schultz-Mattis定理。
When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu–Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be lower than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulae for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. Along the way we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb–Schultz–Mattis theorem.