Some exact excited states in a linear antiferromagnetic spin system

W.J. Caspers

G. Gómez-Santos

The XXZ spin-1/2 Hamiltonian in the linear chain is exactly transformed into a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The ground state of the new Hamiltonian is studied with the Hartree-Fock approximation. This approximation is shown to become exact in the XY and extreme antiferromagnetic limits, with excellent results in between. Known results concerning the existence or nonexistence of long-range order and gap in the excitation spectrum are reproduced by our solution. Good quantitative agreement with representative properties of the exact solution is obtained. The domain-wall Hamiltonian is shown to be the natural framework for the understanding of the ground state and low-lying excited states of the XXZ system in the antiferromagnetic regime.

Kiyomi Okamoto, Hidetoshi Nishimori, Y‐h. Taguchi

We numerically caculate the exact ground state energy E 0 ( N , δ) and the first excited state energy E 1 ( N , δ) of the one-dimensional spin-\(\frac{1}{2}\) alternating antiferromagnetic Heisenberg model

Takehiko Oguchi

W.J. Caspers, Wim Magnus

Andrei A. Zvyagin

It is shown using the exact Bethe-ansatz solution that for a multichain quantum antiferromagnetic spin S =1/2 system the excitation energy has a gap for the version of the model linearized about Fermi points and is gapless for its lattice analog. The result is generalized for multichain spin- S quantum antiferromagnet and for strongly correlated electron models with a “permutation” construction of the supersymmetric Hamiltonians.