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Open AccessArticle

Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, Germany
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Entropy 2020, 22(9), 984; https://doi.org/10.3390/e22090984
Received: 31 July 2020 / Revised: 28 August 2020 / Accepted: 1 September 2020 / Published: 4 September 2020
(This article belongs to the Special Issue Open Quantum Systems (OQS) for Quantum Technologies)
This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30. View Full-Text
Keywords: quantum spin chains; matrix-product states; open quantum systems; many-body systems; numerical methods; quantum stochastic Schrödinger equation; feedback control quantum spin chains; matrix-product states; open quantum systems; many-body systems; numerical methods; quantum stochastic Schrödinger equation; feedback control
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MDPI and ACS Style

Finsterhölzl, R.; Katzer, M.; Knorr, A.; Carmele, A. Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution. Entropy 2020, 22, 984. https://doi.org/10.3390/e22090984

AMA Style

Finsterhölzl R, Katzer M, Knorr A, Carmele A. Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution. Entropy. 2020; 22(9):984. https://doi.org/10.3390/e22090984

Chicago/Turabian Style

Finsterhölzl, Regina; Katzer, Manuel; Knorr, Andreas; Carmele, Alexander. 2020. "Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution" Entropy 22, no. 9: 984. https://doi.org/10.3390/e22090984

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