Simulating correlation-spreading dynamics in the two-dimensional Bose-Hubbard model by the tensor-network method

The recent developments of analog quantum simulators with cold atoms and trapped ions have required cross-checking the accuracy of quantum-simulation experiments using quantitative numerical methods. However, it is particularly challenging to simulate the dynamics of systems with more than one spatial dimension. Here we show that a tensor-network algorithm running on classical computers is practical for this purpose. Specifically, we analyze the dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from a Mott insulator using the tensor-network method based on infinite projected entangled pair states (iPEPS). We have found that the single-particle correlation functions are in good agreement with a recent experiment. We also predict how phase and group velocities change in the intermediate interaction regime by extracting them from the single-particle and density-density correlation functions. These findings provide a quantitative benchmark for future experiments and numerical simulations.