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The Heisenberg antiferromagnet with discrete disorder on an infinite squarelattice is evolved in time from an initial N\'eel state. The simulation isperformed with the neighborhood tensor update (NTU) algorithm for an infiniteprojected entangled pair state (iPEPS) [Phys. Rev. B 104, 094411 (2021)].Ancillary spins are used to average over $2$ or $5$ discrete values ofdisorder. With a bond dimension up to $20$, evolution times are long enough toidentify a many body localized regime for a strong enough disorder.Furthermore, the same Hamiltonian is subject to periodic spin flips.Simulations of the Floquet dynamics show that it can sustain a time crystallinestage for a strong enough disorder.

Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update