We develop randomized matrix-free algorithms for estimating partial traces. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng, Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems, J. Chem. Phys. 157, 064106 (2022)] by deflating important subspaces (e.g. corresponding to the low-energy eigenstates) explicitly. This results in a significant variance reduction for matrices with quickly decaying singular values. We then apply our algorithm to study the thermodynamics of several Heisenberg spin systems, particularly the entanglement spectrum and ergotropy.

翻译：我们开发了用于估计部分迹的随机无矩阵算法。该算法通过显式地压缩重要子空间（例如对应于低能量本征态的子空间），改进了[T. Chen and Y-C. Cheng, Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems, J. Chem. Phys. 157, 064106 (2022)]中基于典型性的方法。对于奇异值快速衰减的矩阵，这能实现显著的方差缩减。随后我们将该算法应用于研究多个Heisenberg自旋系统的热力学性质，特别是纠缠谱与ergotropy。