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Adiabatic connection between the RVB State and the ground state of the half filled periodic Anderson model

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

A one-parameter family of models that interpolates between the periodic A nderson model with infinite repulsion at half-filling and a model whose ground state is exactly the Resonating-Valence-Bond state is studied. It is shown numerically that the excitation gap does not collapse. Therefore the ground states of the two models are adiabatically connected. 1 I.

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A one-parameter family of models that interpolates between the periodic A nderson model with infinite repulsion at half-filling and a model whose ground state is exactly the Resonating-Valence-Bond state is studied. It is shown numerically that the excitation gap does not collapse. Therefore the ground states of the two models are adiabatically connected. 1 I.
The resonant valence-bond state, proposed by Anderson as a possible ground state in certain antiferromagnetic systems, and relevant to the problem of high-temperature superconductivity, is studied by numerical simulation on a finite cluster. It is found to be the ground state of a simple Hubbard model with a half-filled band on a centered hexagon for a range of intermediate values of the electron interaction parameter. A singlet ground state is obtained away from the half-filled limit for the same parameters.
We have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-Tc{T}_{c}Tc​ Cu oxides.
Two spin models in two dimensions are constructed for which the exact ground states can be written down in a certain parameter regime of the Hamiltonian. The ground state of the first model is a local resonating valence bond (RVB) state in which not all the spins participate in resonance. The ground state is highly degenerate and there is a gap in the excitation spectrum. The second model is shown to have a ground state which is a quantum spin liquid with all the spins taking part in resonance. The ground state obtained is non-degenerate and there is no gap in the excitation spectrum.