A Pairwise Connected Tensor Network Representation of Path Integrals

TL;DR

This paper introduces a novel pairwise connected tensor network approach for efficiently representing and evaluating real-time path integrals, improving simulation of quantum systems with non-Markovian environments.

Contribution

A new tensor network method specifically incorporating pairwise influence functional interactions for compact and efficient path integral simulations.

Findings

Demonstrated application to spin-boson models

Compared performance with existing path integral methods

Showed potential for multistate quantum system simulations

Abstract

It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized using matrix product states, taking advantage of the finite length of the non-Markovian memory. Tensor networks promise to provide a new, unified language to express the structure of path integral. Here, a generalized tensor network is derived and implemented specifically incorporating the pairwise interaction structure of the influence functional, allowing for a compact representation and efficient evaluation. This pairwise connected tensor network path integral (PCTNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage requirements and performance are compared with iterative quasi-adiabatic propagator path integral and iterative blip-summed path integral. Finally, the viability of using PCTNPI for simulating multistate problems is demonstrated taking advantage of the compressed representation.