In this paper we give an algebraic construction of the fused model for ABJM spin chain and find the corresponding boost operator. We also investigate the open spin Hamiltonian for fused model and point out the general common structures of the boundary terms.
A general fusion procedure for open gl(N) spin chains: Application to the ABJM spin chain
We formulate a general fusion procedure for open gl(N) spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of gl(N). We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of su(4).
Solving for the integrable boundary states of the ABJM spin chain from KT-relations
We study integrable boundary states of the alternating SU(4) spin chain arising in ABJM theory. Starting from the KT-relation, we directly solve the integrability constraints for states with n-site translational invariance. For odd and even n, these constraints are reduced respectively to state equations and operator equations for the elementary n-site block and the matrix K(u). We analyze chiral and achiral cases for n≤4. In the 1-site case we allow general operator-valued integrable pairs with an internal space, while in the remaining cases we focus on c-number solutions.