  One of the most interesting directions in theoretical high-energy and
condensed-matter physics is understanding dynamical properties of collective
states of quantum field theories. The most elementary tool in this quest is
retarded equilibrium correlators governing the linear response theory. In this
article we examine tensor networks as a way of determining them in a fully ab
initio way in a class of (1+1)-dimensional quantum field theories arising as
infrared descriptions of quantum Ising chains.We show that, complemented with
signal analysis using the Prony method, tensor network calculations for
intermediate times provide a powerful way to explore the structure of
singularities of the correlator in the complex frequency plane and to make
predictions about the thermal response to perturbations in a class of
nonintegrable interacting quantum field theories.
