Construction of a new class of quantum integrable inhomogeneous models

Anjan Kundu

Anjan Kundu

Anjan Kundu

Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at its various realizations and limits can generate a wide range of integrable models. They cover quantum lattice as well as field models associated with the quantum $R$-matrix of trigonometric type or at the undeformed $q \\to 1$ limit similar models belonging to the rational class. The classical limit likewise yields the corresponding classical discrete and field models. Thus along with the generation of known integrable models in a unifying way a new class of inhomogeneous models including variable mass sine-Gordon model, inhomogeneous Toda chain, impure spin chains etc. are constructed.

Anjan Kundu

The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit inhomogeneity. Such models include variable mass sine-Gordon model, cylindrical NLS, spin chains with impurity, inhomogeneous Toda chain, the Ablowitz-Ladik model etc.

Anton Vladimirovich Zabrodin

Anjan Kundu

A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$ matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known discrete and field models a new class of inhomogeneous and impurity models is obtained.