A tensor network representation of path integrals: Implementation and analysis

TL;DR

This paper introduces a tensor network-based method for efficient real-time path integral simulations of quantum systems, demonstrating its effectiveness on various models and highlighting its computational advantages.

Contribution

It presents a novel tensor network path integral (TNPI) approach that efficiently captures non-local interactions and accelerates simulations of complex quantum dynamics.

Findings

Efficient tensor network representation of path integrals for realistic systems

Significant reduction in computational effort using symmetry-based accelerated convergence

Applicable to multi-state systems like FMO and molecular wires

Abstract

Tensors with finite correlation afford very compact tensor network representations. A novel tensor network-based decomposition of real-time path integral simulations involving Feynman-Vernon influence functional is introduced. In this tensor network path integral (TNPI) technique, the finite temporarily non-local interactions introduced by the influence functional can be captured very efficiently using matrix product state representation for the path amplitude (PA) tensor. We illustrate this particular TNPI method through various realistic examples, including a charge transfer reaction and an exciton transfer in a dimer. We also show how it is readily applied to systems with greater than two states by simulating a 7-site model of FMO and a molecular wire model. The augmented propagator (AP) TNPI utilizes the symmetries of the problem, leading to accelerated convergence and dramatic reductions of computational effort. We also introduce an approximate method that speeds up propagation beyond the non-local memory length. Furthermore, the structure imposed by the tensor network representation of the PA tensor naturally suggests other factorizations that make simulations for extended systems more efficient. These factorizations would be the subject of future explorations. The flexibility of the AP-TNPI framework makes it a promising new addition to the family of path integral methods for non-equilibrium quantum dynamics.