Finsterhölzl Regina, Katzer Manuel, Knorr Andreas, Carmele Alexander
Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, Germany.
Entropy (Basel). 2020 Sep 4;22(9):984. doi: 10.3390/e22090984.
This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.
本文提出了一种利用矩阵乘积态（MPS）对开放量子多体系统进行时间演化的高效算法，该算法提出了一种方便的MPS架构结构，它利用了系统和库的初始状态。通过这样做，避免了数值上昂贵的重排序协议。它适用于具有马尔可夫型相互作用的系统，其中只需要考虑库的当前状态。展示了其对多体系统与库之间非马尔可夫型相互作用的适应性，其中在计算中需要包括来自库的信息回流。此外，还展示了量子随机薛定谔图景中基的推导。作为一个范例模型，使用了具有最近邻相互作用的海森堡自旋链。结果表明，该算法能够处理大尺寸系统。作为非马尔可夫型相互作用的一个例子，对于长度为N = 30的链，展示了在具有相干反馈控制的多体系统中产生高度异常的稳态。
