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 Incoming links: Spin-one-half triplet state

Two-spin Heisenberg Hamiltonian in an opposing longitudinal field 2026-10-03

For two spin-one-half particles,

H = α S^{(1)} \cdot S^{(2)} + B (S_{z}^{(1)} - S_{z}^{(2)})

has two eigenvalues

α ℏ^{2} /4

and two further eigenvalues

- \frac{α ℏ ^{2}}{4} \pm B^{2} ℏ^{2} + \frac{α ^{2} ℏ ^{4}}{4} .

For positive

α

, the zero-field limit has a unique spin-one-half singlet state ground state and a triply degenerate spin-one-half triplet state excited level.

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