Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution
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 pro...
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MDPI AG
2020-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/9/984 |
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| author | Regina Finsterhölzl Manuel Katzer Andreas Knorr Alexander Carmele |
| author_facet | Regina Finsterhölzl Manuel Katzer Andreas Knorr Alexander Carmele |
| author_sort | Regina Finsterhölzl |
| collection | DOAJ |
| description | 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 <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>30</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T16:34:43Z |
| format | Article |
| id | doaj.art-3e9dca6113fb4ebabef8febd2c14671b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T16:34:43Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3e9dca6113fb4ebabef8febd2c14671b2023-11-20T12:34:11ZengMDPI AGEntropy1099-43002020-09-0122998410.3390/e22090984Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-EvolutionRegina Finsterhölzl0Manuel Katzer1Andreas Knorr2Alexander Carmele3Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, GermanyInstitut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, GermanyInstitut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, GermanyInstitut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, GermanyThis 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 <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>30</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/1099-4300/22/9/984quantum spin chainsmatrix-product statesopen quantum systemsmany-body systemsnumerical methodsquantum stochastic Schrödinger equation |
| spellingShingle | Regina Finsterhölzl Manuel Katzer Andreas Knorr Alexander Carmele Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution Entropy quantum spin chains matrix-product states open quantum systems many-body systems numerical methods quantum stochastic Schrödinger equation |
| title | Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution |
| title_full | Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution |
| title_fullStr | Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution |
| title_full_unstemmed | Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution |
| title_short | Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution |
| title_sort | using matrix product states for open quantum many body systems efficient algorithms for markovian and non markovian time evolution |
| topic | quantum spin chains matrix-product states open quantum systems many-body systems numerical methods quantum stochastic Schrödinger equation |
| url | https://www.mdpi.com/1099-4300/22/9/984 |
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