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arXiv:cond-mat/9706203 · Journal of Physics Condensed Matter

The adiabatic connection between the resonating-valence-bond state and the ground state of the half-filled periodic Anderson model

Kensuke Kimura, Yasuhiro Hatsugai, Mahito Kohmoto

Published Nov 24, 1997• 0 citations
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Abstract

A one-parameter family of models interpolates between the periodic Anderson model with infinite repulsion at half-filling and a model whose ground state is exactly the resonating-valence-bond state. It is shown numerically that the excitation gap does not collapse. Therefore the ground states of the two models are adiabatically connected.

DOI
10.1088/0953-8984/9/47/005

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A one-parameter family of models interpolates between the periodic Anderson model with infinite repulsion at half-filling and a model whose ground state is exactly the resonating-valence-bond state. It is shown numerically that the excitation gap does not collapse. Therefore the ground states of the two models are adiabatically connected.
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.
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.
The diagrammatic valence-bond technique is adopted to investigate one-dimensional half-filled Hubbard chains with long-range e-e interactions and alternating charge-transfer integrals. Exact results for finite-size systems with different boundary conditions are carefully extrapolated to the infinite-chain limit. In addition to various ground-state properties, such as bond-charge-density wave and bond-order amplitude, we calculate the optical gap and the corresponding oscillator strength. We introduce adiabatic phonons able to modulate on-site energies and investigate the stability of the system with respect to site-charge-density wave distortion. We also evaluate the response of the electronic system to the perturbation induced by adiabatic phonons which modulate charge-transfer integrals, and calculate the corresponding screening of vibrational frequencies.