CoChat
Sign Up
Cited by 24Quantum many-body systemsCold Atom Physics and Bose-Einstein CondensatesQuantum Mechanics and Applications

Continuous matrix product states with periodic boundary conditions and an application to atomtronics

Open access
Draxler, Damian, Haegeman, Jutho, Verstraete, Frank, Rizzi, Matteo·2017·Physical Review B
DOI 10.1103/physrevb.95.045145
Open this paper in CoChat — free accountOpen PDF

Abstract

We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system---an interacting Bose gas rotating in a ring shaped trap in the presence of a localized barrier potential.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevb.95.045145

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The differential equation from TDVP in non-uniform cMPS can be interpreted as a non-commuting version of the Gross-Pitaevskii equation.

    “The differential equation that follows from the TDVP equation in this non-uniform setting can be interpreted as a non-commuting version of the Gross-Pitaevskii equation [67].”

    From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [67]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 34

  1. R. Orus, Ann. Phys. 349, 117 (2014). · DOI · Paper page
  2. F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 104, 190405 (2010). · DOI
  3. J. Haegeman, J. I. Cirac, T. J. Osborne, and F. Verstraete, Phys. Rev. B 88, 085118 (2013). · DOI
  4. A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, Phys. Rev. Lett. 106, 130401 (2011). · DOI
  5. K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Phys. Rev. Lett. 110, 025302 (2013). · DOI
  6. S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London) 506, 200 (2014). · DOI
  7. B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, Phys. Rev. A 75, 023615 (2007). · DOI
  8. D. W. Hallwood, T. Ernst, and J. Brand, Phys. Rev. A 82, 063623 (2010). · DOI
  9. M. C. Beeler, R. A. Williams, K. Jimenez-Garcia, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, Nature (London) 498, 201 (2013). · DOI
  10. E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963). · DOI
  11. C.-N. Yang and C. Yang, J. Math. Phys. 10, 1115 (1969). · DOI
  12. V. Korepin, N. Bogoliubov, and A. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, Cambridge, 1997).
  13. F. W. J. Hekking and L. I. Glazman, Phys. Rev. B 55, 6551 (1997). · DOI
  14. K. A. Matveev, A. I. Larkin, and L. I. Glazman, Phys. Rev. Lett. 89, 096802 (2002). · DOI
  15. M. Cominotti, D. Rossini, M. Rizzi, F. Hekking, and A. Minguzzi, Phys. Rev. Lett. 113, 025301 (2014). · DOI
  16. P. Dirac, On the Annihilation of Electrons and Protons (Math- ematical Proceedings of the Cambridge Philosophical Society, Cambridge, 1930).
  17. J. Frenkel, Wave Mechanics, Advanced General Theory (Oxford University Press, Oxford, 1934).
  18. J. Kramer and M. Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics (Springer, Berlin, 1981).
  19. J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011). · DOI · Paper page
  20. P. Hauke and L. Tagliacozzo, Phys. Rev. Lett. 111, 207202 (2013). · DOI
  21. J. Haegeman, D. Draxler, V. Stojevic, J. I. Cirac, T. J. Osborne, and F. Verstraete, arXiv:1501.06575. · arXiv
  22. D. Draxler, J. Haegeman, T. J. Osborne, V. Stojevic, L. Vanderstraeten, and F. Verstraete, Phys. Rev. Lett. 111, 020402 (2013). · DOI
  23. F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004). · DOI
  24. P. Pippan, S. R. White, and H. G. Evertz, Phys. Rev. B 81, 081103 (2010). · DOI
  25. B. Pirvu, F. Verstraete, and G. Vidal, Phys. Rev. B 83, 125104 (2011). · DOI
  26. J. Haegeman, J. I. Cirac, T. J. Osborne, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 105, 251601 (2010). · DOI · Paper page
  27. J. Haegeman, M. Marien, T. J. Osborne, and F. Verstraete, J. Math. Phys. 55, 021902 (2014). · DOI · Paper page
  28. A. Milsted, J. Haegeman, and T. J. Osborne, Phys. Rev. D 88, 085030 (2013). · DOI · Paper page
  29. J. Haegeman, T. J. Osborne, and F. Verstraete, Phys. Rev. B 88, 075133 (2013). · DOI · Paper page
  30. F. Bloch, Phys. Rev. A 7, 2187 (1973). · DOI
  31. M. A. Cazalilla, J. Phys. B 37, S1 (2004). · DOI
  32. M. Gerster, P. Silvi, M. Rizzi, R. Fazio, T. Calarco, and S. Montangero, Phys. Rev. B 90, 125154 (2014). · DOI
  33. S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadzibabic, Phys. Rev. Lett. 110, 025301 (2013). · DOI
  34. S. S. Chung, K. Sun, and C. J. Bolech, Phys. Rev. B 91, 121108 (2015). · DOI

Cited by

Sorted by citations

Authors
Draxler, D., Haegeman, J., Verstraete, F., & Rizzi, M.
Affiliations
  • University of Vienna (AT)
  • Ghent University (BE)
  • Johannes Gutenberg University Mainz (DE)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2017-01-30
Volume
95
Issue
4
ISSN
  • 2469-9950 (ISSN-L)
  • 2469-9969
DOI
10.1103/physrevb.95.045145
OpenAlex
W2592748449
Cited by
24
References
1
Citations by year
2026: 1 · 2025: 2 · 2024: 1 · 2023: 2 · 2022: 4 · 2021: 2 · 2020: 2 · 2019: 5 · 2018: 3 · 2017: 2
FWCI
1.61
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B./Physical review. B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
  • Austrian Science Fund (F4104 SFB ViCoM, F4014 SFB FoQuS)
  • Deutsche Forschungsgemeinschaft (OSCAR RI2345/2-1)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
continuous matrix product states, periodic boundary conditions, Dirac-Frenkel variational principle, one-dimensional quantum field theory, translation invariance, quantum impurity problems, atomtronics, rotating Bose gases, interacting Bose gas

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review