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arXiv · 2201.05529

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

Gerald E. Fux·Dainius Kilda·Brendon W. Lovett·Jonathan Keeling
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Abstract

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.

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Gerald E. Fux, Dainius Kilda, Brendon W. Lovett, Jonathan Keeling. 2022-01-14. Tensor network simulation of chains of non-Markovian open quantum systems. https://doi.org/10.1103/physrevresearch.5.033078

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