Integrability of Heisenberg Chain

Natan Andrei, Henrik Johannesson

Bo-Yu Hou, Kangjie Shi, Rui‐Hong Yue +1 more

We show the integrability of spin-½ XXZ Heisenberg chain with two arbitrary spin boundary impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these models are obtained by the means of Bethe ansatz method.

Stefan Groha, Fabian H L Essler

Abstract Integrable models support elementary excitations with infinite lifetimes. In the spin-1/2 Heisenberg chain these are known as spinons. We consider the stability of spinons when a weak integrability breaking perturbation is added to the Heisenberg chain in a magnetic field. We focus on the case where the perturbation is a next nearest neighbour exchange interaction. We calculate the spinon decay rate in leading order in perturbation theory using methods of integrability and identify the dominant decay channels. The decay rate is found to be small, which indicates that spinons remain well-defined excitations even though integrability is broken.

N. Papanicolaou

Haldane (1982) conjectured that a simple generalisation of the Heisenberg spin chain leads to a completely integrable classical system without invoking the usual continuum approximation. Complete integrability is established for the generalised discrete chain by exhibiting a Lax pair and an infinite set of non-local conservation laws. The associated inverse scattering problem is also formulated providing explicit soliton solutions.

E.J. Van Dongen, Hans W. Capel, Th.J. Siskens