arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2409.04145quant-phcond-mat.mes-hallphysics.comp-ph
收藏

连通性至关重要:张量网络态模拟开放量子系统中浴模排序与几何结构的影响

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

Thibaut Lacroix, Brendon W. Lovett, Alex W. Chin

AI总结:

本研究针对开放量子系统多环境模拟的张量网络拓扑优化问题,发现简单玻色浴模排序可降低矩阵乘积态收敛所需键维,证明复杂拓扑分析非必需且树张量网络态常次优。

摘要:

研究与多个环境相互作用的量子系统动力学,在从量子化学、量子热力学到非平衡系统等诸多场景中都具有重要意义。针对这类问题,基于张量网络的方法是开展数值精确模拟的最先进方法。然而,要在多环境、非微扰的场景下高效使用这些方法,需要对波函数拟设的拓扑结构进行优化选择,这通常通过分析不同系统与环境自由度之间的互相关来实现。本文针对典型模型哈密顿量证明:使{系统+环境}联合态可写为矩阵乘积态的玻色环境模简单排序,尽管会引入长程相互作用,但能显著降低收敛所需的键维数。这些结果表明,在许多重要的物理开放系统模型中,通常无需为调整张量网络拓扑(如纠缠重整化)进行复杂的相关性分析,且树张量网络态相比简单矩阵乘积态是次优的。

英文摘要:

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 Ansätze. 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑