PT - Journal Article
AU - Watanabe, Haruki
DP - 2020
TI - Counting Rules of Nambu–Goldstone Modes
TA - Annual Review of Condensed Matter Physics,
VI - 11
IP - Volume 11, 2020
PG - 169-187
AID - 10.1146/annurev-conmatphys-031119-050644
SO - Annual Review of Condensed Matter Physics 2020;11(1):169-187
AB - 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.,
4099- https://www.annualreviews.org
4100- https://www.annualreviews.org/content/journals/10.1146/annurev-conmatphys-031119-050644