Sublattice entanglement in an exactly solvable anyonlike spin ladder

Abstract

We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sub-lattices), such that the scattering phases are constants: particles of the same type scatter as free fermions, whereas the inter-particle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sub-lattice entanglement by numerical means.

Free fermions beyond Jordan and Wigner

“…We here first review the earlier procedure, and then explain how to generalise it to our Hamiltonians. The relation (21) between the generators proves absolutely essential.…”

“…All hope is not lost: we can exploit the fact not all terms in the Hamiltonian are independent, as shown in (21). First consider Q (2) , which as seen in ( 34) is the sum over all products of two commuting generators.…”

“…There are two types of such joints. One is similar to (56), and so we again exploit (45) and the identity (21) with no need of swapping. The joints of this type in the cancelling cases pictured as e.g.…”

“…Here we cannot use (21) directly without any swap. Instead, the cancelling configuration does not have a joint, but rather a forbidden pair A j B j in the middle of an odd-length path.…”

“…The cancellations discussed in section 3.3 that do not require a swap (i.e. only utilise (21)) apply here as well. Thus the arguments given above in (56) or (57, 58) also mean the analogous even-length paths also cancel two by two.…”