A scaling approach to two-magnon excitations in general S quantum spin chains is presented. The local densities of two-magnon excitations can be obtained directly without solving the one-magnon problem beforehand. Special features of the excitation spectrum are related to the complete integrability of the model.
Quantum spin chains of higher spin are interesting in the case of both ferromagnets and antiferromagnets. They comprise a wide range of model types—Bethe–Ansatz integrable, nonintegrable, and with limited integrability. It is not well appreciated that the two-magnon (two-body) problems is always solvable, by Bethe–Ansatz and Green’s-function techniques, regardless of the integrability character of the entire model, with interesting implications in the context of solitons and bound solitons. Chubukov and Kveschenko have suggested using the two-magnon problem in a test for integrability and claim to find additional classes of integrable spin chains for s=1 and s= (3)/(2) . Here we investigate this situation.
The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.
Abstract We calculate exactly the entanglement content of magnon excited states in the integrable spin-1/2 XXX and XXZ chains in the scaling limit. In particular, we show that as far as the number of excited magnons with respect to the size of the system is small one can decompose the entanglement content, in the scaling limit, to the sum of the entanglement of particular excited states of free fermionic or bosonic theories. In addition we conjecture that the entanglement content of the generic translational invariant free fermionic and bosonic Hamiltonians can be also classified, in the scaling limit, with respect to the entanglement content of the fermionic and bosonic chains with the number operator as the Hamiltonian in certain circumstances. Our results effectively classify the entanglement content of wide range of integrable spin chains in the scaling limit.