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

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.

15 pages, 14 figures

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Cited by in corpus (29)

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• Sublinear scaling in non-Markovian open quantum systems simulations
• Many-Body Open Quantum Systems
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• Process tensor approaches to modeling two-dimensional spectroscopy
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• Process tensor distinguishability measures
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• Scalable tensor network algorithm for quantum impurity problems
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