$\mu$-Symmetry Breaking : Algebraic Approach to Finding Building Blocks of Quantum Many-body Systems
Sho Higashikawa, Masahito Ueda · arXiv (Cornell University) · 2015
One of the most fundamental problems in quantum many-body systems is the identification of a mean field in spontaneous symmetry breaking which is usually done in a heuristic manner. We propose a systematic method of finding a mean field based on the Lie algebra by introducing a class of symmetry broken phases which we call simple $\mu$-symmetry breaking. We also show that the number of Nambu-Goldstone modes with both linear and quadratic dispersion relations and the homotopy group of topological excitations can be determined systematically for simple $\mu$-symmetry breaking.