  It was found that renormalization group equations in the heavy-quark
effective theory (HQET) for the operators involving one effective heavy quark
and light degrees of freedom are completely integrable in some cases and are
related to spin chain models with the Hamiltonian commuting with the
nondiagonal entry $C(u)$ of the monodromy matrix. In this work we provide a
more complete mathematical treatment of such spin chains in the QISM framework.
We also discuss the relation of integrable models that appear in the HQET
context with the large-spin limit of integrable models in QCD with light
quarks. We find that the conserved charges and the "ground state" wave
functions in HQET models can be obtained from the light-quark counterparts in a
certain scaling limit.
