Transport through (non)-conformal defect

I will discuss simple microscopic realizations of the conformal and non-conformal defects in 1+1 dimensional systems. First, I review the transport through the link defect in 1D tight-binding fermionic chains. I show how to present full-counting statistics (FCS) in terms of Fredholm determinants and how to use microscopic bosonization to get its large time asymptotic. Knowing FCS allows us to address various physical quantities such as current through the link, the shot noise, and the entanglement entropy. Further, I will do small adjustments and turn the link defect into the conformal defect, which is characterized by a constant transmission coefficient at all energies. I discuss how physics is changed in this case and address the driven conformal defect. If time permits, I will discuss how the interaction between fermions changes the picture.