Exact correlation functions at finite temperatures in a Tomonaga-Luttinger liquid with an open end

The authors derive here exact analytic expressions for correlations in Tomonaga-Luttinger liquids with a boundary at finite temperature and discuss two distinct regimes: Coulomb and Hund metals. The difference between Coulomb and Hund is in the value of $K$. It is found that only the Hund metal has a peak in the single-particle density of states on its edge. Peak splitting due to coupling with plasmon polaritons is also studied. This shows how boundaries and external environmental coupling can shape the local density of states.