Comparison of Three Self-Consistent Ground States for the Linear Heisenberg Antiferromagnet

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Abstract
The attractive interactions in the fermion representation of the linear Heisenberg antiferromagnet lead to three qualitatively different self‐consistent ground states. In addition to the Hartree–Fock solution, Ruijgrok and Rodriguez have obtained an ordered state with lower energy. A new self‐consistent solution, without long‐range order but with lower energy than the Hartree–Fock, is discussed. The new solution agrees well with numerical estimates for the spin correlations among nearest, second, and third nearest neighbors. The correlations between the parallel and transverse spin components are also compared. This previously overlooked test indicates that all three self‐consistent solutions are strongly anisotropic. They are axially symmetric and, in spite of excellent ground‐state energies, poor representations of the spherically symmetric, singlet ground state. The possibility of three qualitatively different approximate ground states, each of too low symmetry, complicates the computation of finite‐temperature properties.
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