Vertex perturbations for the Luttinger model

The Luttinger model plays a central role in condensed matter physics, as it is believed that it captures universal features of a wide class of interacting, one-dimensional Fermi systems. It was solved by Mattis and Lieb in 1965 using bosonization, and its exact solvability makes the model a natural starting point for studying perturbations of interacting one-dimensional systems.

In this talk I discuss vertex perturbations of the Luttinger model, expressed as exponentials of bosonic fields. The main focus is on constructing a convergent perturbative expansion for the partition function. The expansion is formulated directly in terms of bosonic correlation functions, and relies on a thermal Wick theorem for vertex operators. Moreover, by adapting the iterated Mayer expansion to this setting, we establish the existence of the thermodynamic limit for the pressure.