Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model

TL;DR

This paper demonstrates that tensor-network methods can accurately simulate the real-time dynamics of the two-dimensional Bose-Hubbard model, providing valuable benchmarks for quantum simulation experiments.

Contribution

It introduces a tensor-network approach using infinite projected entangled pair states to analyze 2D Bose-Hubbard dynamics, bridging classical simulations and quantum experiments.

Findings

Good agreement with recent experimental correlation functions

Predicted variation of phase and group velocities in moderate interactions

Provides quantitative benchmarks for future experiments

Abstract

Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly challenging for dynamics of systems with more than one spatial dimension. Here we demonstrate that a tensor-network method running on classical computers is useful for this purpose. We specifically analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from the Mott insulator by means of the tensor-network method based on infinite projected entangled pair states. Calculated single-particle correlation functions are found to be in good agreement with a recent experiment. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region, which serves as a quantitative benchmark for future experiments and numerical simulations.