论文标题
强烈耦合开放量子系统的平衡还原密度矩阵的数值计算
Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
论文作者
论文摘要
我们描述了一种数值算法，用于近似于平衡还原密度矩阵和有效（平均力）哈密顿量的有效（平均力）哈密顿量，用于一组系统旋转与一组浴缸相结合时，当总系统（System+BATH）保持在尺寸的热量平衡中时，由弱耦合与“超级阶段”。我们的方法是通过痕量估计器和Krylov子空间方法来计算裸量子系统的量子期望值的现在标准典型算法的概括。特别是，我们的算法利用了以下事实：在给定的随机状态下测量浴缸时，降低的系统密度倾向于集中于相应的热力学平均系统密度。进行理论误差分析和数值实验以验证我们算法的准确性。进一步的数值实验证明了我们用于应用方法的潜力，包括研究量子相变和远程相互作用系统的纠缠熵。
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is held in canonical thermal equilibrium by weak coupling with a "super-bath". Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long-range interaction systems.
