Quantum inverse scattering method

Definition

Let $V = \C^2$ be the auxiliary space and let $\mathcal{H} = V_1 \otimes \dots \otimes V_N$ be the quantum space, a tensor product of copies $V_n$ of $\C^2$. Let $R(\lambda) \in \End(V \otimes V)$, for $\lambda \in \C$, be a solution of the Yang–Baxter equation with spectral parameter: $$R_{12}(\lambda - \mu) R_{13}(\lambda) R_{23}(\mu) = R_{23}(\mu) R_{13}(\lambda) R_{12}(\lambda - \mu).$$ The method consists of the following steps.

1. Choose Lax operators $L_{0n}(\lambda) \in \End(V_0 \otimes V_n)$ that satisfy $R_{00'}(\lambda - \mu) L_{0n}(\lambda) L_{0'n}(\mu) = L_{0'n}(\mu) L_{0n}(\lambda) R_{00'}(\lambda - \mu)$, where $V_0, V_{0'}$ are two copies of $V$.
2. Form the monodromy matrix $T_0(\lambda) = L_{0N}(\lambda) \cdots L_{01}(\lambda)$ and the transfer matrix $t(\lambda) = \tr_0 T_0(\lambda) \in \End(\mathcal{H})$, the partial trace over $V_0$.
3. Write $T_0(\lambda) = \begin{pmatrix} A(\lambda) & B(\lambda) \\ C(\lambda) & D(\lambda) \end{pmatrix}$ with entries in $\End(\mathcal{H})$. Take a reference vector $\Omega$ with $C(\lambda) \Omega = 0$ for all $\lambda$. Look for eigenvectors of all $t(\mu)$ of the form $B(\lambda_1) \cdots B(\lambda_M) \Omega$.