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physica status solidi (b)

Symmetry and Eigenstates of the 3D Hubbard Model in an Electromagnetic Field

Gang Su, Mo‐Lin Ge

Published Nov 1, 1991• 3 citations
Publisher

Abstract

Abstract The symmetry and the eigenstates of the 3D Hubbard model in the presence of an external electromagnetic field on a periodic simple cubic lattice are investigated within the pseudospin and spin framework. It is shown that the magnetic flux through the periodic lattice is quantized in units of hc/2e, and in this situation the Hubbard system possesses SO4 symmetry which is proved to be spontaneous breaking in the eigenstates obtained explicitly of the model. The information of ODLRO in those eigenstates is also discussed. The absolute ground state of the Hubbard model is yet obtained, and found that the state may not show superconducting transition.

DOI
10.1002/pssb.2221680126

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Physical review. B, Condensed matter•Nov 15, 1993•1 citation
Abstract The symmetry and the eigenstates of the 3D Hubbard model in the presence of an external electromagnetic field on a periodic simple cubic lattice are investigated within the pseudospin and spin framework. It is shown that the magnetic flux through the periodic lattice is quantized in units of hc/2e, and in this situation the Hubbard system possesses SO4 symmetry which is proved to be spontaneous breaking in the eigenstates obtained explicitly of the model. The information of ODLRO in those eigenstates is also discussed. The absolute ground state of the Hubbard model is yet obtained, and found that the state may not show superconducting transition.
By means of the Bethe-ansatz method, the one-dimensional Hubbard model with repulsive on-site coupling in an external magnetic field is solved exactly. It is found that the energy of the ground state depends on the magnetic flux \ensuremath{\varphi} through the ring formed by a periodic lattice chain, and the lowest-energy state corresponds to \ensuremath{\varphi}=n(hc/2e), with n an integer and -e the electron charge. The calculations illustrate that the strongly correlated Hubbard ring with periodic boundary conditions in its ground state is a superconducting ring. It can also be shown that the system possesses an internal SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) symmetry.
The Hubbard model with unit concentration of electrons per one site in the external magnetic field H is considered. In the H\ensuremath{\rightarrow}\ensuremath{\infty} limit the ground state is ferromagnetic and dielectric. A decrease of H results in the phase transition to a new ground state. The electric properties of this state depend on (1) the lattice dimensionality and (2) the U/t ratio (U,t are the standard parameters of the Hubbard model). The linear [one-dimensional (1D)], square (2D), and simple cubic (3D) lattices are considered. In the 1D and 2D cases the new ground state is always dielectric. In the 3D case this state is dielectric only at U/(12t)>${\mathit{W}}^{\mathrm{\ensuremath{-}}1}$, where W=1.516. . . is the Watson integral. At U/(12t)${\mathit{W}}^{\mathrm{\ensuremath{-}}1}$ it becomes a conducting one. The line of phase transition with respect to the field is constructed in the H-U coordinates. It is found that the transition to the dielectric state results in the transformation of the ferromagnetic order to the spin-flip phase. The transition to the conducting state results only in a decrease of the average local spin.