Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model

TL;DR

This paper explores tensor network methods, specifically matrix product states, to efficiently compute equilibrium correlation functions in open quantum systems like the spin-boson model, introducing new steady state techniques.

Contribution

It introduces a steady state formulation using influence functionals and MPS for calculating equilibrium correlations, advancing tensor network approaches in open quantum systems.

Findings

Steady state influence functional approach effectively computes equilibrium correlations.

Multiple contour methods are compared for real-time correlation calculations.

Steady state method avoids complex time contours, simplifying computations.

Abstract

We investigate the application of matrix product state (MPS) representations of the influence functionals (IF) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.