Pseudospin symmetry and new collective modes of the Hubbard model

The Hubbard model possesses a SU (2) pseudospin symmetry, which contains the U (1) phase symmetry as a subgroup. The existence of such symmetry leads to interesting experimental consequences if the U (1) phase symmetry is spontaneously broken, i. e. , if the ground state is superconducting. In this case, there must exist a pair of massive collective modes which together with the usual Goldstone mode form a triplet representation of the psuedospin group. These collective modes are collisionless and couple directly to external charge disturbances with wave number and can therefore be detected experimentally as sharp resonances.