Speaker
Jose Carmelo
(Department of Physics, University of Minho)
Description
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).
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).
