Constructing Tensor Network Influence Functionals for General Quantum Dynamics

TL;DR

This paper introduces a tensor network approach to compute influence functionals for complex quantum dynamics, enabling longer and more accurate simulations by exploiting low bond dimension approximations in certain regimes.

Contribution

It develops an iterative tensor network formalism for influence functionals applicable beyond linear bath couplings, demonstrating efficient approximability in specific dynamical regimes.

Findings

Influence functionals can be approximated with low bond dimension tensor networks.

The method allows longer time simulations than traditional approaches.

Correlations in the influence functional can temporarily increase before decreasing during iteration.

Abstract

We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of the bond dimensions and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.