Small matrix disentanglement of the path integral: Overcoming the exponential tensor scaling with memory length

Research output: Contribution to journalArticlepeer-review

Abstract

The discretized path integral expression for the reduced density matrix (RDM) of a system interacting with a dissipative harmonic bath is fully entangled because of influence functional terms that couple the variables at different time points. The iterative decomposition of the path integral, which exploits the finite length of influence functional memory, involves a tensor propagator whose size grows exponentially with the memory length. The present Communication disentangles the path integral by recursively spreading the temporal entanglement over longer path segments, while decreasing its contribution. Eventually, the entangled term becomes sufficiently small and may be neglected, leading to iterative propagation of the RDM through simple multiplication of matrices whose size is equal to that of the bare system. It is found that the temporal entanglement length is practically equal to the bath-induced memory length. The small matrix decomposition of the path integral (SMatPI) is stable and very efficient, extending the applicability of numerically exact real-time path integral methods to multi-state systems.

Original languageEnglish (US)
Article number041104
JournalJournal of Chemical Physics
Volume152
Issue number4
DOIs
StatePublished - Jan 31 2020

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Fingerprint Dive into the research topics of 'Small matrix disentanglement of the path integral: Overcoming the exponential tensor scaling with memory length'. Together they form a unique fingerprint.

Cite this