Quantum correlation functions through tensor network path integral

TL;DR

This paper introduces a tensor network path integral method for efficiently calculating equilibrium correlation functions in open quantum systems, enabling simulations of larger, strongly interacting systems at lower temperatures.

Contribution

It develops a novel tensor network approach tailored for equilibrium correlation functions using path integrals, extending the applicability to larger and more complex quantum systems.

Findings

Efficient representation of path integrals for open quantum systems.

Application to rate theory and spin correlation functions.

Enhanced simulation capabilities at lower temperatures.

Abstract

Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for calculation of eigenstates. Recently, it has been shown that a variety of these networks can be leveraged to make real time non-equilibrium simulations of dynamics involving the Feynman-Vernon influence functional more efficient. In this work, tensor networks are utilized for calculating equilibrium correlation function for open quantum systems using the path integral methodology. These correlation functions are of fundamental importance in calculations of rates of reactions, simulations of response functions and susceptibilities, spectra of systems, etc. The influence of the solvent on the quantum system is incorporated through an influence functional, whose unconventional structure motivates the design of a new optimal matrix product-like operator that can be applied to the so-called path amplitude matrix product state. This complex time tensor network path integral approach provides an exceptionally efficient representation of the path integral enabling simulations for larger systems strongly interacting with baths and at lower temperatures out to longer time. The design and implementation of this method is discussed along with illustrations from rate theory, symmetrized spin correlation functions, dynamical susceptibility calculations and quantum thermodynamics.