August 30, 2010 to September 24, 2010
Europe/Stockholm timezone

Extended global symmetry of the Hubbard model on bipartite lattices

Sep 3, 2010, 11:00 AM
132:028 (Nordita)




Jose Carmelo (Department of Physics, University of Minho)


J. M. P. Carmelo, Stellan Östlund, and M. J. Sampaio The Hubbard model on a bipartite lattice is one of the most studied many- particle quantum problems. However, except in one dimension the model has no exact solution and there remain many open questions about its properties. Here we report a recent exact result [1]. According to it, for on-site interaction U 6= 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral t = 0 studied in [2] can be lifted to a global [SU(2)× SU(2)× U(1)]/Z2 2 = SO(3) ×SO(3) ×U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated- electron number of singly-occupied sites operator. Although addition of chemicalpotential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its energy eigenstates refer to representations of the new found global SO(3) × SO(3) × U(1) = [SO(4) × U(1)]/Z2 symmetry, which is expected to have important physical consequences. Our studies reveal that for U/4t > 0 the model charge and spin degrees of freedom are associated with U(2) = SU(2) × U(1) and SU(2) symmetries [1], respectively, rather than with two SU(2) symmetries. (The latter case would hold if the model global symmetry was only SO(4) = [SU(2) ×SU(2)]/Z2.) The occurrence of such charge U(2) = SU(2) × U(1) symmetry and spin SU(2) symmetry is for the onedimensional model behind the different ABCDF and ABCD forms of the charge and spin monodromy matrices, respectively, found by the inverse scattering method exact solution [3].
1. J.M.P. Carmelo, Stellan Östlund, and M.J. Sampaio, Ann.Phys. 325, 1550 (2010).
2. Stellan Östlund and Eugene Mele, Phys.Rev. B 44, 12413 (1991).
3. M.J. Martins and P.B. Ramos, Nucl.Phys. B 522, 413 (1998).

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