The scattering matrix for a generalgl(2) spin chain

Abstract

We study the general L 0 -regular gl(2) spin chain, i.e. a chain where the sites {i, i + L 0 , i + 2L 0 , . . . } carry the same arbitrary representation (spin) of gl(2). The basic example of such chain is obtained for L 0 = 2, where we recover the alternating spin chain. Firstly, we review different known results about their integrability and their spectrum. Secondly, we give an interpretation in terms of particles and conjecture the scattering matrix between them.

Modified Algebraic Bethe Ansatz: Twisted XXX Case

“…3 Explicit Hamiltonian for this case is not known. It can be formulated in the more restrictive case of L0-regular spin chains [5], where L0 arbitrary positive (half)-integer spins are periodically repeated. The case L0 = 1 with spin 1 2 corresponds to the Hamiltonian (1.1).…”

“…The MABA allows us to construct the modified Bethe vector keeping the highest or lowest weight vectors as a starting point. The idea of the modified algebraic Bethe ansatz [1,2,3,4,7] relies in the construction of modified operators that preserve the operator algebra structure 5 . The transformation of the monodromy matrix…”