Prof. José Manuel Pereira Carmelo
Center of Physics, University of Minho, Portugal
carmelo@fisica.uminho.pt
Abstract: At onsite repulsion U = 0 the global symmetry of the half-filled Hubbard model on a bipartite lattice is O(4) = SO(4) x Z2. Here the factor Z2 refers to a transformation under which the model Hamiltonian is not invariant for U ≠ 0. C. N. Yang and S. C. Zhang considered the most natural possibility that for U > 0 the SO(4) symmetry inherited from the U = 0 Hamiltonian O(4) = SO(4) x Z2 symmetry was the model global symmetry. While that the model contains such a SO(4) symmetry is an exact result, a recent study of the problem by the author and collaborators revealed an extra exact hidden global U(1) symmetry emerging for U ≠ 0, in addition to SO(4). Specifically, the model extended global symmetry is found to be [SO(4) x U(1)]/ Z2 = SO(3) x SO(3) x U(1) = [SU(2) x SU(2) x U(1)]/ Z. The factor 1/ Z in [SU(2) x SU(2) x U(1)]/ Z22 imposes that both [Ss + Sc] and [Sη + Sc] are integer numbers. Here Sη, Ss, and Sc are the η-spin, the spin, and the eigenvalue of the generator of the new global U(1) symmetry, respectively. The latter is found in to be one half the numbers of rotated-electron singly occupied sites. The corresponding electron-rotated-electron unitary transformation plays a major role in the model physics. Since the chemical-potential and magnetic-field operator terms commute with the Hamiltonian, for all densities its energy eigenstates refer to representations of the new found global symmetry. In this talk I introduce the latter symmetry and report its consequences for the one-dimensional (1D) lattice. The exact Bethe-ansatz solution quantum numbers are found to label specific occupancy configurations of rotated-electron related objects. Such occupancy configurations arise naturally as representations of the extended global symmetry. That the zero-momentum forward-scattering collisions of the emerging objects control the finite-energy features observed by angle-resolved photoemission on quasi-1D metals is justified on the basis of a related pseudofermion dynamical theory.
Location: 606 Conference Room
Date and time: September 9th, 2011 10:30 A.M—11:30 A.M