String Theory Journal Club

The XXZ model is a well-known example of the q-deformed model that can be constructed using an R matrix. However, there are different ways of constructing different types of q-deformed models. To obtain Hamiltonians, we use a coproduct from a Hopf algebra structure to generate higher-order Casimir elements. Moreover, we show different representations using diagrammatic Temperley-Lieb (TL) operators, which reveal topological properties of the considered Hamiltonians. We show different classes of Hamiltonians of integrable and non-integrable systems that can be produced using Hopf and TL algebras. Besides the ground state, we employ a topological basis structure to obtain excited states.We also discuss an alternative way of acquiring q-deformed Hamiltonians using matrix product states.