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Physics Letters A

An RVB approach to the Hubbard model

G. M. Cicuta, Sebastiano Stramaglia

Published Jun 1, 1992• 3 citations
Publisher
DOI
10.1016/0375-9601(92)90347-o

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The concept of the resonating valence bond (RVB) state was originally proposed by Anderson (1987) for the ground state of the positive-U Hubbard model. However, the on-site pairing long-range order is expected to exist in the ground state of the negative-U Hubbard model and to be incompatible with the RVB order. In this article, we shall rigorously prove that, in fact, these two long-range orderings either coexist or are suppressed simultaneously in the global ground states of the doped Hubbard models.

Journal of Physics A Mathematical and General•Oct 21, 1994•3 citations
This paper compares the kinetic energy of holes in the antiferromagnetic (AF) state and in an approximate singlet liquid wave function of the Resonating Valence Bond type (RVB), with only nearest neighbour singlet pairing. The atomic interaction U of the Hubbard model is taken to be large compared with the band width 8 t . In the limit 8 t / U →0, I find that the hole kinetic energy is at most as low in RVB than in AF, but there are indications that it is in fact lower in AF. At finite t / U , the comparison between AF and RVB depends on corrections of order t / U which are not known yet for RVB, but which should be of the same order as in AF. As a restult within the simplest Hubbard model with nearest neighbour hopping, it is unlikely that a small concentration of holes can stabilize RVB if the latter is less stable than AH at half band filling.
The Hubbard model in the strong-coupling regime is studied by the Kondo-lattice theory. If no symmetry is broken at a sufficiently low temperature in sufficiently low dimensions, an electron liquid is stabilized by the Fock-type exchange effect of the superexchange interaction. Since the stabilization mechanism is none other than the resonating-valence-bond (RVB) mechanism, the electron liquid is none other than an RVB electron liquid. The RVB electron liquid in the Hubbard model is adiabatically connected to the RVB spin liquid in the Heisenberg model.
The concept of the resonating valence bond (RVB) state was originally proposed by Anderson (1987) for the ground state of the positive-U Hubbard model. However, the on-site pairing long-range order is expected to exist in the ground state of the negative-U Hubbard model and to be incompatible with the RVB order. In this article, we shall rigorously prove that, in fact, these two long-range orderings either coexist or are suppressed simultaneously in the global ground states of the doped Hubbard models.