Haldane–Shastry model
# Haldane–Shastry model

In statistical physics, the Haldane–Shastry model is a spin chain model, 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. It is an exactly solvable model, and was exactly solved by Shastry.

## Formulation

For a chain with $N$ spin 1/2 sites, the quantum phase space is described by the Hilbert space ${\mathcal {H}}=(\mathbb {C} ^{2})^{\otimes N}$. The Haldane–Shastry model is described by the Hamiltonian

$H_{\mathrm {HS} }={\frac {1}{2}}\sum _{m<n}^{N}{\frac {J_{0}}{\sin ^{2}{n\pi /N}}}{\vec {\sigma }}_{m}\cdot {\vec {\sigma }}_{n}.$

