Light-cones in many-body open quantum systems with memory

Abstract:Memory effects in many-body quantum systems interacting with an environment significantly impact their behavior. Nevertheless, much of our understanding of many-body open quantum systems is based on models within the Born-Markov approximation where these effects are neglected. In this paper, we consider a general class of spatially local open quantum lattice models with a non-Markovian environment that is approximated as Gaussian. Our main result is a set of Lieb-Robinson bounds for such models. For models where the environment has independent local baths, we show that the Lieb-Robinson velocity is controlled by one-norm of the memory kernel within the evolution time-interval, yielding a linear light cone whenever the memory kernel has a bounded one-norm. For models where excitations can propagate through the environment, we prove a polynomial light cone that captures bath-mediated acceleration of information spreading. In both of these cases, we show that the derived Lieb-Robinson bounds are tight by also constructing lattice models saturating these bounds. Finally, we consider the problem of approximating a non-Markovian model by a larger Markovian model, which contains the system spins together with only a finite number of bosonic environment modes. We establish that as a consequence of our Lieb-Robinson bounds, the number of environment modes {per system site} needed to accurately capture local observables is independent of the size of the system.

arXiv:2410.15481 [quant-ph]

(or arXiv:2410.15481v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2410.15481 Focus to learn more arXiv-issued DOI via DataCite

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