Applying the Variational Principle to (1+1)-Dimensional Quantum Field Theories
Open accessAbstract
We extend the recently introduced continuous matrix product state variational class to the setting of (1+1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman concerning the application of the variational procedure to relativistic theories, and provides a new way to regularize quantum field theories. A fermionic version of the continuous matrix product state is introduced which is manifestly free of fermion doubling and sign problems. We illustrate the power of the formalism by studying the momentum occupation for free massive Dirac fermions and the chiral symmetry breaking in the Gross-Neveu model.
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.
Integrity signals
Registry
Cites
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.
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 largest eigenvalue of the transfer-matrix excitation eigenvalue equation defines the gap of the transfer matrix and is related to the correlation length of the two-dimensional tensor network.
“The largest eigenvalue defines the gap of the transfer matrix, and is related to the correlation length of the two-dimensional tensor network [61].”
From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [61]
A generic method for contracting overlaps of tangent vectors was introduced in Ref [61].
“A generic method for contracting overlaps of tangent vectors -a crucial ingredient in any tangent-space method -was introduced in Ref. [61], and a benchmark of the quasiparticle excitation ansatz was performed [85].”
From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [61]
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
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323 · see citing works
Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensionsPreprint
Verstraete, F., & Cirac, J. I. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/0407066 · Cited by 672 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 21
- R. P. Feynman, Proceedings of the International Workshop on Variational Calculations in Quantum Field Theory held in Wangarooge, West Germany (L. Polley and D. E. L. Pottinger, eds.), World Scientific Publishing, Singapore, pp. 28-40 (1987).
- D. Karabali, C. Kim, V.P. Nair, Phys.Lett. B 434, 103 (1998);
- D.R. Campagnari, H. Reinhardt, Phys. Rev. D 82, 105021 (2010);
- M. Fannes, B. Nachtergaele, R. F. Werner, Commun. Math. Phys. 144, 443 (1992);
- S. Ostlund, S. Rommer, Phys. Rev. Lett. 75, 3537 (1995);
- F. Verstraete, D. Porras, J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004).
- F. Verstraete, J. I. Cirac, V. Murg, Adv. Phys. 57, 143 (2008);
- J. I. Cirac, F. Verstraete, J. Phys. A: Math. Theor. 42, 504004 (2009).
- G. Vidal, Phys. Rev. Lett. 99, 220405 (2007);
- R. Hübener, C. Kruszynska, L. Hartmann, W. Dür, Phys. Rev. A 79, 022317 (2009).
- T.M.R. Byrnes, P. Sriganesh, R.J. Bursill, C.J. Hamer, Phys. Rev. D 66, 013002 (2002);
- T. Sugihara, JHEP 5, 007 (2004);
- D.J. Weir, Phys. Rev. D 82, 025003 (2010).
- F. Verstraete, J. I. Cirac, Phys. Rev. Lett. 104, 190405 (2010).
- I. Maruyama, H. Katsura, J. Phys. Soc. Jpn. 79, 073002 (2010).
- R. Jackiw in Conformal Field Theory, Anomalies, and Superstrings, First Asia Pacific Workshop on High Energy Physics (C. K. Chew et al., eds.), World Scientific Publishing, Signapore (1987)
- T. J. Osborne, J. Eisert and F. Verstraete, Phys. Rev. Lett. 105, 260401 (2010).
- F. Verstraete J. I. Cirac, Phys. Rev. B 73, 094423 (2006);
- T. J. Osborne, Phys. Rev. Lett. 97, 157202 (2006);
- J. Eisert, M. Cramer, M. B. Plenio, Rev. Mod. Phys. 82, 277 (2010).
- K. A. Milton, The Casimir Effect: Physical Manifestations of Zero-Point Energy, World Scientific, Singapore (2001).
Cited by
Sorted by citations
Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255 · see citing works
Tangent-space methods for uniform matrix product states
Vanderstraeten, L., Haegeman, J., & Verstraete, F. (2019) · SciPost Physics Lecture Notes · doi:10.21468/scipostphyslectnotes.7 · Cited by 233 · see citing works
“[68].”
Self-citation
- Authors
- Haegeman, J., Cirac, J. I., Osborne, T. J., Verschelde, H., & Verstraete, F.
- Affiliations
- Ghent University (BE)
- Max Planck Institute of Quantum Optics (DE)
- Institute for Advanced Study (DE)
- University of Vienna (AT)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-12-16
- Volume
- 105
- Issue
- 25
- Pages
- 251601-251601
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2072083256
- Cited by
- 59
- References
- 2
- Citations by year
- 2026: 1 · 2024: 2 · 2023: 4 · 2022: 3 · 2021: 8 · 2020: 1 · 2019: 7 · 2018: 3 · 2017: 9 · 2016: 3 · 2015: 6 · 2014: 6 · 2013: 3 · 2012: 3
- FWCI
- 1.03
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- 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)
- PoS
- Funders
- Deutsche Forschungsgemeinschaft
- Universität Wien
- Fonds Wetenschappelijk Onderzoek
- Vlaamse regering
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- variational principle, continuous matrix product states, 1+1 dimensional quantum field theory, relativistic quantum field theory, fermion doubling, sign problem, chiral symmetry breaking, Gross-Neveu model
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
