Tensor network simulation of chains of non-Markovian open quantum systems

Gerald E. Fux, Dainius Kilda, Brendon W. Lovett, Jonathan Keeling

Research output: Contribution to journalArticlepeer-review


We introduce a general numerical method to compute dynamics and multi-time correlations of chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for general (possibly non-Markovian) open quantum systems with time evolving block decimation (TEBD) for 1D chains. It systematically reduces the numerical complexity originating from system-environment correlations before integrating them into the full many-body problem, making a wide range of applications numerically feasible. We illustrate the power of this method by studying two examples. First, we study the thermalization of individual spins of a short XYZ Heisenberg chain with strongly coupled thermal leads. Our results confirm the complete thermalization of the chain when coupled to a single bath, and reveal distinct effective temperatures in low, mid, and high frequency regimes when the chain is placed between a hot and a cold bath. Second, we study the dynamics of diffusion in an longer XY chain, when each site couples to its own bath.
Original languageEnglish
Article number033078
Number of pages14
JournalPhysical Review Research
Issue number3
Early online date4 Aug 2023
Publication statusPublished - 4 Aug 2023


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