Abstract
The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems. Its applicability has so far been limited to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles, equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy, and long-time stability. Moreover, the technique can directly be implemented in other approaches such as Green’s function, stochastic, and pseudomode formulations. As one highly nontrivial application, for the subohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.
- Received 18 February 2022
- Accepted 8 November 2022
- Corrected 21 March 2023
DOI:https://doi.org/10.1103/PhysRevLett.129.230601
© 2022 American Physical Society
Physics Subject Headings (PhySH)
Corrections
21 March 2023
Correction: The omission of a support statement in the Acknowledgments section has been fixed.