Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States

TL;DR

This paper introduces a novel numerical method combining Feynman path integrals and matrix product states to efficiently simulate real-time dynamics of lattice polarons in one and two dimensions.

Contribution

The authors develop a flow equation approach that compresses the integrand as a low bond dimension MPS, enabling efficient computation of polaron dynamics and spectral functions.

Findings

Accurate spectral functions in 1D benchmarked against existing results.

Successful extension to 2D spectral functions.

Demonstrated capability to simulate polaron diffusion in 1D and 2D.

Abstract

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.