Infinite tensor networks for (1+1)d quantum field theories: lattice QED and chiral ladders

In this talk I will first make a broad introduction to tensor network states and methods together with an overview of some recent developments. Afterwards, I will focus on recent applications of infinite-size tensor network methods in the study of some (1+1)d quantum field theories. Specifically, I will focus on the infinite-DMRG algorithm to simulate (i) (1+1)d QED, using U(1) gauge invariance, and (ii) a chiral ladder Hamiltionian with SU(2) symmetry and a CFT description at low energies. Implications of the results will also be discussed.