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Counting Rules of Nambu–Goldstone Modes
Annual Review of Condensed Matter Physics ( IF 14.3 ) Pub Date : 2020-03-16 , DOI: 10.1146/annurev-conmatphys-031119-050644
Haruki Watanabe 1
Affiliation  

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.

中文翻译:


Nambu-Goldstone模式的计数规则

当整体连续对称性自发地破裂时,会出现称为Nambu-Goldstone模式(NGM)的无间隙集体激励,这些激励控制着系统的低能特性。这个著名的定理的应用范围从高能粒子物理学到凝聚态和原子物理学。当在缺乏洛伦兹不变性的系统中发生对称破坏时(通常在凝聚态系统中就是这种情况),生成的NGM的数量可能会少于破坏的对称生成器的数量,并且NGM的扩散不一定是线性的。在本文中,我们回顾了最近建立的与破碎的内部对称性相关的NGM公式,这些公式在相对论和非相对论系统中均有效。我们还讨论了源自时空对称破坏的NGM的复杂性。在此过程中,我们涵盖了来自各种上下文的许多启发性示例。我们还从里伯-舒尔茨-马蒂斯定理中提出了一种互补的观点。

更新日期:2020-04-21
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