The space of integrable systems from generalised T(T)over-bar-deformations

We introduce an extension of the generalised T (T) over bar -deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.

Automated summary

We extend the generalised T(T) over bar-deformation model to include the complete set of extensive charges. The results show that this model can generate deformations of S-matrices beyond the traditional factors and can have arbitrary functional dependence on momenta. Additionally, we derive the flow equations for free energy and all free energy fluxes from basic principles, which demonstrates that the thermodynamics of the deformed models can be described by integral equations of the thermodynamic Bethe-Ansatz.