Summing real time Feynman paths of lattice polarons with matrix product states

We study numerically the real time dynamics of lattice polarons by combining the Feynman path integral and the matrix product state (MPS) approach. By constructing and solving a flow equation, we show that the integrand, viewed as a multivariable function of polaron world line parameters, can be compressed as a low bond dimension MPS, thereby allowing for efficient evaluation of various dynamical observables. We establish the effectiveness of our method by benchmarking the calculated polaron spectral function in one dimension against available results. We further demonstrate its potential by presenting the polaron spectral function in two dimensions and simulating polaron diffusion in both one and two dimensions.