In quantum statistical physics, the Haldane–Shastry model is a spin chain, defined on a one-dimensional, periodic lattice.
Unlike the prototypical Heisenberg spin chain, which only includes interactions between neighboring sites of the lattice, the Haldane–Shastry model has long-range interactions, that is, interactions between any pair of sites, regardless of the distance between them.
The model is named after and was defined independently by Duncan Haldane and B. Sriram Shastry.
[1][2] It is an exactly solvable model, and was exactly solved by Shastry.
spin 1/2 sites, the quantum phase space is described by the Hilbert space
The Haldane–Shastry model is described by the Hamiltonian
σ →
σ →
denotes the Pauli vector at the
th site (acting nontrivially on the
Note that the pair potential suppressing the interaction strength at longer distances is an inverse square
the chord distance between the
th sites viewed as being equispaced on the unit circle.