Haldane–Shastry model
Appearance
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.[1][2] It is an exactly solvable model, and was exactly solved by Shastry.[2]
Formulation
For a chain with spin 1/2 sites, the quantum phase space is described by the Hilbert space . The Haldane–Shastry model is described by the Hamiltonian
See also
References
- ^ Haldane, F. D. M. (15 February 1988). "Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-1/2 antiferromagnetic Heisenberg chain with 1/r^2 exchange". Physical Review Letters. 60 (7): 635–638. doi:10.1103/PhysRevLett.60.635. Retrieved 19 July 2023.
- ^ a b Shastry, B. Sriram (15 February 1988). "Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions". Physical Review Letters. 60 (7): 639–642. doi:10.1103/PhysRevLett.60.639. Retrieved 19 July 2023.