  The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev.
Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute
the ground state of one-dimensional quantum lattice systems in the
thermodynamic limit. Here we extend the algorithm to tackle a much broader
class of problems, namely the simulation of arbitrary one-dimensional evolution
operators that can be expressed as a (translationally invariant) tensor
network. Relatedly, we also address the problem of finding the dominant
eigenvalue and eigenvector of a one-dimensional transfer matrix that can be
expressed in the same way. New applications include the simulation, in the
thermodynamic limit, of open (i.e. master equation) dynamics and thermal states
in 1D quantum systems, as well as calculations with partition functions in 2D
classical systems, on which we elaborate. The present extension of the
algorithm also plays a prominent role in the infinite projected entangled-pair
states (iPEPS) approach to infinite 2D quantum lattice systems.
