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：暂无翻译