Abstract
The ground state of the one-dimensional antiferromagnetic Heisenberg-Ising model coupled with the lattice distortion is determined based on the phase Hamiltonian defined by the boson representation of the spinless fermions. This phase Hamiltonian can describe properly the possible feature of the resonating valence bond proposed by Anderson. All the possible states, including the spin-Peierls state, the Neel state, and states with both lattice distortions and magnetic orderings, are examined within the self-consistent harmonic approximation by use of the treatment of Nakano and Fukuyama which extends the theory of spin-Peierls state of Cross and Fisher. The phase boundary for small Ising anisotropy is determined which separates the spin-Peierls state and the Neel state, and it is found that the former state is stable in a wide region of parameters.
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