Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

Time evolution of an infinite 2D many body quantum lattice system can be described by the Suzuki-Trotter decomposition applied to the infinite projected entangled pair state (iPEPS). Each Trotter gate increases the bond dimension of the tensor network, $D$, that has to be truncated back in a way that minimizes a suitable error measure. This paper goes beyond simplified error measures -- like the one used in the full update (FU), the simple update (SU), and their intermediate neighborhood tensor update (NTU) -- and directly maximizes an overlap between the exact iPEPS with the increased bond dimension and the new iPEPS with the truncated one. The optimization is performed in a tangent space of the iPEPS variational manifold. This gradient tensor update (GTU) is benchmarked by a simulation of a sudden quench of a transverse field in the 2D quantum Ising model and the quantum Kibble-Zurek mechanism in the same 2D system.