Connectivity matters: Impact of bath modes ordering and geometry in open quantum system simulation with Tensor Network States

TL;DR

This paper demonstrates that simple ordering of bath modes in tensor network simulations of open quantum systems can significantly reduce computational complexity, challenging the need for complex correlation-based topology optimizations.

Contribution

It shows that straightforward mode ordering in tensor network states often outperforms complex correlation analysis for simulating open quantum systems.

Findings

Mode ordering reduces bond dimension needed for convergence.

Simple matrix product states outperform tree tensor networks in key models.

Correlation analysis for topology optimization may be unnecessary.

Abstract

Being able to study the dynamics of quantum systems interacting with several environments is important in many settings ranging from quantum chemistry to quantum thermodynamics, through out-of-equilibrium systems. For such problems tensor network-based methods are state-of-the-art approaches for performing numerically exact simulations. However, to be used efficiently in this multi-environment and non-perturbative context, these methods require an optimized choice of the topology of the wave-function Ans\"atze. This is often done by analysing cross-correlations between different system and environment degrees of freedom. Here, we show for canonical model Hamiltonians that simple orderings of bosonic environmental modes, which enable the joint {System + Environments} state to be written as a matrix product state, considerably reduce the bond dimension required for convergence despite introducing long-ranged interactions. These results suggest that complex correlation analyses for tweaking tensor networks topology (e.g. entanglement renormalization) are usually not necessary and that tree tensor network states are sub-optimal compared to simple matrix product states in many important models of physical open systems.