A typical quantum state obeying the area law for entanglement on an infinite
2D lattice can be represented by a tensor network ansatz -- known as an
infinite projected entangled pair state (iPEPS) -- with a finite bond dimension
D. Its real/imaginary time evolution can be split into small time steps. An
application of a time step generates a new iPEPS with a bond dimension k
times the original one. The new iPEPS does not make optimal use of its enlarged
bond dimension kD, hence in principle it can be represented accurately by a
more compact ansatz, favourably with the original D. In this work we show how
the more compact iPEPS can be optimized variationally to maximize its overlap
with the new iPEPS. To compute the overlap we use the corner transfer matrix
renormalization group (CTMRG). By simulating sudden quench of the transverse
field in the 2D quantum Ising model with the proposed algorithm, we provide a
proof of principle that real time evolution can be simulated with iPEPS. A
similar proof is provided in the same model for imaginary time evolution of
purification of its thermal states.Comment: 9 pages, 10 figures, replaced with the published versio