Algebraic Bethe ansatz for seven-vertex model

The work is dedicated to the construction of algebraic Bethe ansatz for seven-vertex model. $R$-matrix of the system is obtained by means of twist from six-vertex model consider by us earlier. The presence of seven nonzero element in $R$-matrix complicates the situation. In particular the commutation relations of elements of monodromy matrix becomes more difficult in comparison with the six-vertex model. But we construct algebraic Bethe ansatz by help of introducing of new operator that is the difference between two operators on the main diagonal of monodromy matrix. The eigenstates and the spectrum of the system were found. This is the first step on the way of comparison of the systems with six- and seven-vertex $R$-matrix respectively.