Abstract
The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ℤd is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ℤd itself.
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Albanese, C. On the spectrum of the Heisenberg Hamiltonian. J Stat Phys 55, 297–309 (1989). https://doi.org/10.1007/BF01042601
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DOI: https://doi.org/10.1007/BF01042601