Counting Rule for Nambu-Goldstone Modes in Nonrelativistic Systems

The counting rule for Nambu-Goldstone modes is discussed using Mori's projection operator method in nonrelativistic systems at zero and finite temperatures. We show that the number of Nambu-Goldstone modes is equal to the number of broken charges, Q(a), minus half the rank of the expectation value of [Q(a), Q(b)]. DOI: 10.1103/PhysRevLett.110.091601