Construction of a new class of quantum integrable inhomogeneous models

Integrable inhomogenous or impurity models are usually constructed by either shifting the spectral parameter in the Lax operator or using another representation of the spin algebra. We propose a more involved general method for such construction in which the Lax operator contains generators of a novel quadratic algebra, a generalization of the known quantum algebra. In forming the monodromy matrix, we can replace any number of the local Lax operators with different realizations of the underlying algebra, which can result in spin chains with nonspin impurities causing changed coupling across the impurity sites, as well as with impurities in the form of bosonic operators. Following the same idea, we can also generate integrable inhomogeneous versions of the generalized lattice sine-Gordon model, nonlinear Schrödinger equation, Liouville model, relativistic and nonrelativistic Toda chains, etc.