Orateur
Description
Luttinger liquid theory offers a powerful framework for understanding one-dimensional quantum systems of bosons, fermions, and spins. A central prediction of this theory is the universal power-law behavior of correlation functions, with exponents determined by a single parameter tied to the system’s thermodynamics. While these universal features are well established, the precise, non-universal details require more refined tools. In this talk, I will explain how such details can be obtained from combinatorial methods based on the finite-size scaling of the matrix elements and how these techniques can be extended to capture subleading asymptotics and treat finite-temperature behavior. As concrete examples, I will focus on strongly interacting systems where correlation functions take an elegant form involving Fredholm determinants of generalized sine kernels.