CoChat
Sign Up
Cited by 104Quantum many-body systemsQuantum Computing Algorithms and ArchitectureTheoretical and Computational Physics

Entanglement renormalization and gauge symmetry

Open access
Tagliacozzo, L., Vidal, G.·2011·Physical Review B
DOI 10.1103/physrevb.83.115127
Open this paper in CoChat — free accountOpen PDF

Abstract

A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a ${Z}_{2}$ lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to $16\ifmmode\times\else\texttimes\fi{}16$ sites (${16}^{2}\ifmmode\times\else\texttimes\fi{}2=512$ spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.

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.83.115127

Cites

99 of 99 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?

  • In two dimensions, DMRG and TTN work only for reasonably small systems.

    “In 2D the situation is more complex - similar to exact diagonalization, DMRG and TTN work only for reasonably small systems [80-82]”

    From Can one trust quantum simulators? (2012) · cites this paper as [80]

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: 40

  1. 73 D. Gottesman, Ph.D. thesis, Caltech(1997).
  2. 79 G. Vidal, arXiv:0912.1651v2(2009). · arXiv
  3. 85 S. Singh, R. N. C. Pfeifer, and G. Vidal, arXiv:0907.2994v1(2009). · arXiv
  4. 86 E. Fradkin and S. Raby, Physical Review D 20 , 2566 (Nov. 1979).
  5. 95 M. D'Elia and L. Tagliacozzo, Phys. Rev. D74 , 114510 (2006), arXiv:hep-lat/0609018. · arXiv
  6. 97 J.-H. Liu, Q.-Q. Shi, H.-L. Wang, J. Links, and H.-Q. Zhou, arXiv.org:0909.3031(2009).
  7. 105 I. S. Tupitsyn, A. Kitaev, N. V. Prokof'ev, and P. C. E. Stamp, arXiv:0804.3175(2008). · arXiv
  8. 106 S. Bravyi, M. Hastings, and S. Michalakis, arXiv:1001.0344v1(2010). · arXiv
  9. 107 J. Vidal, S. Dusuel, and K. P. Schmidt, arXiv:0807.0487(Jul. 2008). · arXiv
  10. 108 J. Vidal, R. Thomale, K. P. Schmidt, and S. Dusuel, arXiv:0902.3547(Feb. 2009), phys. Rev. B 80, 081104 (2009). · arXiv
  11. 109 T. Nishino and K. Okunishi, Journal of the Physical Society of Japan 65 , 891 (1996).
  12. 111 X. Chen, Z.-C. Gu, and X.-G. Wen, arXiv:1004.3835v1(2010). · arXiv
  13. 118 A. Bazavov, C. Bernard, C. DeTar, S. Gottlieb, U. M. Heller, J. E. Hetrick, J. Laiho, L. Levkova, P. B. Mackenzie, M. B. Oktay, R. Sugar, D. Toussaint, and R. S. V. de Water, 0903.3598(Mar. 2009), arXiv:0903.3598 . · arXiv
  14. 126 F. Verstraete and J. I. Cirac, arXiv:cond- mat/0407066v1(2004).
  15. 138 G. Sierra and M. A. Martin-Delgado, arXiv:condmat/9811170(Nov. 1998).
  16. 139 N. Maeshima, Y. Hieida, Y. Akutsu, T. Nishino, and K. Okunishi, cond-mat/0101360(2001), Phys.Rev.E64:016705,2001. · arXiv
  17. 140 Y. Nishio, N. Maeshima, A. Gendiar, and T. Nishino, arXiv:cond-mat/0401115(2004). · arXiv
  18. 150 F. Mezzacapo and J. I. Cirac, arXiv:1006.4480v2(2010). · arXiv
  19. 151 S.-H. Li, Q.-Q. Shi, and H.-Q. Zhou, arXiv:1001.3343v1(2010). · arXiv
  20. 159 N. Read and S. Sachdev, International Journal of Modern Physics B 5, 219(1991), arXiv:cond-mat/0402109v1 . · arXiv
  21. 160 S. Sachdev, Lectures at the Les Houches School on 'Modern theories of correlated electron systems', France, May 2009(2009), arXiv:1002.3823v2 . · arXiv
  22. 164 N. Schuch, I. Cirac, and D. Perez-Garcia, arXiv:1001.3807v2(2010). · arXiv
  23. 165 B. Swingle and X.-G. Wen, arXiv:1001.4517v1(2010). · arXiv
  24. 166 X. Chen, B. Zeng, Z.-C. Gu, I. L. Chuang, and X.-G. Wen, arXiv:1003.1774v1(2010). · arXiv
  25. 168 I. P. McCulloch and M. Gulacsi, EPL (Europhysics Letters) 57 , 852 (2002).
  26. 170 P. Buividovich and M. Polikarpov, Physics Letters B 670 , 141 (2008), ISSN 0370-2693.
  27. 173 L. D. D. A. Di Giacomo and G. Paffuti, Physics Letters B 349 , 513 (1995), arXiv:hep-lat/9403013 . · arXiv
  28. 174 I. Montvay and G. Munster cambridge, UK: Univ. Pr. (1994) 491 p. (Cambridge monographs on mathematical physics).
  29. 185 D. Gottesman, Ph.D. thesis, Caltech(1997).
  30. 191 G. Vidal, arXiv:0912.1651v2(2009). · arXiv
  31. 197 S. Singh, R. N. C. Pfeifer, and G. Vidal, arXiv:0907.2994v1(2009). · arXiv
  32. 198 E. Fradkin and S. Raby, Physical Review D 20 , 2566 (Nov. 1979).
  33. 207 M. D'Elia and L. Tagliacozzo, Phys. Rev. D74 , 114510 (2006), arXiv:hep-lat/0609018. · arXiv
  34. 209 J.-H. Liu, Q.-Q. Shi, H.-L. Wang, J. Links, and H.-Q. Zhou, arXiv.org:0909.3031(2009).
  35. 217 I. S. Tupitsyn, A. Kitaev, N. V. Prokof'ev, and P. C. E. Stamp, arXiv:0804.3175(2008). · arXiv
  36. 218 S. Bravyi, M. Hastings, and S. Michalakis, arXiv:1001.0344v1(2010). · arXiv
  37. 219 J. Vidal, S. Dusuel, and K. P. Schmidt, arXiv:0807.0487(Jul. 2008). · arXiv
  38. 220 J. Vidal, R. Thomale, K. P. Schmidt, and S. Dusuel, arXiv:0902.3547(Feb. 2009), phys. Rev. B 80, 081104 (2009). · arXiv
  39. 221 T. Nishino and K. Okunishi, Journal of the Physical Society of Japan 65 , 891 (1996).
  40. 223 X. Chen, Z.-C. Gu, and X.-G. Wen, arXiv:1004.3835v1(2010). · arXiv

Cited by

Sorted by citations

Related

Authors
Tagliacozzo, L., & Vidal, G.
Affiliations
The University of Queensland (AU)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2011-03-16
Volume
83
Issue
11
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.83.115127
OpenAlex
W2049932646
Cited by
104
References
99
Citations by year
2026: 5 · 2025: 4 · 2024: 7 · 2023: 2 · 2022: 4 · 2021: 7 · 2020: 14 · 2019: 9 · 2018: 7 · 2017: 8 · 2016: 5 · 2015: 4 · 2014: 13 · 2013: 5 · 2012: 6
FWCI
4.85
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • arXiv (Cornell University)
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 › Condensed Matter Physics › Theoretical and Computational Physics
Keywords
entanglement renormalization, gauge invariance, lattice gauge theory, Z2 lattice gauge theory, toric code, magnetic field, coarse-graining, variational ansatz, ground-state phase diagram, deconfinement, quantum phase transitions, Wilson loops, ground-state fidelity, effective field theory

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