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Communications in Theoretical Physics

Investigation on the Ground State of the Hubbard Model

Gang Su, Mo‐Lin Ge

Published Jan 1, 1992• 3 citations
Publisher

Abstract

The absolute ground states of the Hubbard model are explicitly presented within the framework of pseudospin when and . It is shown that the states do not possess true off-diagonal long-range order in the two cases. It is also discovered that in the ground states the phase symmetry of the Hubbard model is spontaneously broken away from the half-filling, and the total spin is zero, which is independent of the sign of U and the electron filling in the considered periodic lattice.

DOI
10.1088/0253-6102/17/1/1

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Physical review. B, Condensed matter•Jan 1, 1994•0 citations
The absolute ground states of the Hubbard model are explicitly presented within the framework of pseudospin when and . It is shown that the states do not possess true off-diagonal long-range order in the two cases. It is also discovered that in the ground states the phase symmetry of the Hubbard model is spontaneously broken away from the half-filling, and the total spin is zero, which is independent of the sign of U and the electron filling in the considered periodic lattice.
In this article, we study off-diagonal long-range order in the negative-U Hubbard model. We rigorously prove that all the elements of the two-particle reduced density matrix are positive, which may indicate a Bose condensation at q=0. Furthermore, we shall show that the ground state at half filling has pseudospin number 0. It implies that a sufficient condition proposed by Yang and Zhang [Int. J. Mod. Phys. B 5, 977 (1991)], for a state \ensuremath{\Psi} having off-diagonal long-range order, may not be a necessary condition.
In this paper, we discuss the physical consequences of pseudospin SU(2)-symmetry breaking in a negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, this will lead to a charge-density-wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have off-diagonal long-range order, signalling a superconductor. In this case, CDW and superconductivity coexist and form a supersolid. Finally, we show that CDW suppress, but do not destroy superconductivity.
A group of analytical wave functions is confirmed to be the ground state of a Hubbard model on a double-layer square lattice in the case of half-filling and in the case with one or two doped holes for a range of parameters. The method is based on the variational principle, and no approximations are applied. In the case of half-filling, the ground state is a product of local pairs. In the case of one or two holes, the doped holes are freely moving in the above background. In both cases there exists a long-range order of the evenness and oddness with respect to the layer parity.