On the complete-spectrum characterization of quantum integrable spin   chains via the inhomogeneous T-Q relation
  With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the corresponding transfer matrix; (2) each eigenvalue of the transfer matrix can be parameterized by a minimal inhomogeneous T-Q relation. These statements hold for both with and without inhomogeneity. The proof can be generalized to other finite-dimensional quantum integrable models. 
Junpeng Cao, Wen-Li Yang, Kangjie Shi and Yupeng Wang
cond-mat.stat-mech hep-th math-ph math.MP