Construction of a new class of quantum integrable inhomogeneous models

Integrable inhomogeneous or impurity models are usually constructed by eith er shifting the spectral parameter in the Lax operator or using another rep resentation of the spin algebra. We propose a more involved general method for such construction in which the Lax operator contains generators of a no vel quadratic algebra, a generalization of the known quantum algebra. in fo rming the monodromy matrix, we can replace any number of the local Lax oper ators with different realizations of the underlying algebra, which can resu lt in spin chains with nonspin impurities causing changed coupling across t he impurity sites, as well as with impurities in the form of bosonic operat ors. Following the same idea, we can also generate integrable inhomogeneous versions of the generalized lattice sine-Gordon model, nonlinear Schroding er equation, Liouville model, relativistic and nonrelativistic Toda chains, etc.