  We propose a new method for computing the ground state properties and the
time evolution of infinite chains based on a transverse contraction of the
tensor network. The method does not require finite size extrapolation and
avoids explicit truncation of the bond dimension along the evolution. By
folding the network in the time direction prior to contraction, time dependent
expectation values and dynamic correlation functions can be computed after much
longer evolution time than with any previous method. Moreover, the algorithm we
propose can be used for the study of some non-invariant infinite chains,
including impurity models.
