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

• URL: http://arxiv.org/abs/2409.04145v2
• Date: Wed, 21 May 2025 12:36:53 GMT
• Title: Connectivity matters: Impact of bath modes ordering and geometry in open quantum system simulation with Tensor Network States
• Authors: Thibaut Lacroix, Brendon W. Lovett, Alex W. Chin,
• Abstract summary: tensor network-based methods are state-of-the-art approaches for performing numerically exact simulations.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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