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Cited by 1,098Quantum many-body systemsQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems

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Verstraete, F., García-Ripoll, J. J., Cirac, J. I.·2004·Physical Review Letters
DOI 10.1103/physrevlett.93.207204
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Abstract

We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of matrix product states which is variational.

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Crossref · 10.1103/physrevlett.93.207204

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  • The transfer matrix is a completely positive map, with the MPS matrices A^s playing the role of Kraus operators.

    “From its definition it follows that the transfer matrix is a completely positive map [9], where the MPS matrices A s play the role of Kraus operators.”

    From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [9]

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Research works printed but not linked: 17

  1. S.R.White, Phys. Rev. Lett. 69, 2863 (1992).
  2. S.R.White, Phys. Rev. B 48, 10345 (1992).
  3. See, for example, Density-Matrix Renormalization, Eds. I. Peschel, et al., (Springer Verlag, Berlin, 1999).
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  8. M. A. Cazalilla, and J. B. Marston, Phys. Rev. Lett. 88, 256403 (2002).
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  10. S. R. White, and A. E. Feiguin, cond-mat/0403310. · arXiv
  11. G. Vidal et al., Phys. Rev. Lett. 90, 227902 (2003).
  12. S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995);
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  14. M. Fannes, B. Nachtergaele and R.F. Werner, Comm. Math. Phys. 144, 443 (1992).
  15. F. Verstraete, D. Porras and J.I. Cirac, cond-mat/0404706. · arXiv
  16. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. 92, 087201 (2004).
  17. C.W. Gardiner and P. Zoller, Quantum noise, Springer- Verlag Berlin (2000).

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Authors
Verstraete, F., García-Ripoll, J. J., & Cirac, J. I.
Affiliations
Max Planck Institute of Quantum Optics (DE)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2004-11-12
Volume
93
Issue
20
Pages
207204-207204
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.93.207204
OpenAlex
W1550516781
Cited by
1,098
References
2
Citations by year
2026: 47 · 2025: 82 · 2024: 91 · 2023: 84 · 2022: 82 · 2021: 87 · 2020: 117 · 2019: 67 · 2018: 56 · 2017: 57 · 2016: 51 · 2015: 38 · 2014: 33 · 2013: 39 · 2012: 21
FWCI
11.87
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • arXiv (Cornell University)
Funders
Deutsche Forschungsgemeinschaft (SFB 631)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
matrix product states, quantum dissipation, thermal equilibrium, one-dimensional quantum systems, mixed states, variational approximation, imaginary time evolution, inhomogeneous systems

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