Cold Atom Simulation of Interacting Relativistic Quantum Field Theories
Open accessAbstract
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
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Relativistic extensions of the Kronig-Penney model have been discussed by several authors, and the impact of relativity on band structure and localization, such as shrinkage of bulk bands with increasing band number, has been highlighted.
“Relativistic extensions of the Kronig-Penney model (also referred to as the Dirac-Kronig-Penney model) have been discussed by several authors (see, for instance, [65,66,67,68,69,70, 71,72,73,74,75,76] and references therein), and the impact of relativity on the band structure and localization, such as shrinkage of the bulk bands with increasing band number, have been highlighted on many occasions.”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [71]
The paper’s discussion of its optical-lattice model (pp. 1–2) describes a low-energy Dirac dispersion, but does not identify the model as a relativistic Kronig–Penney extension. Searches for Kronig–Penney, localization, and shrinking bulk bands found no passage addressing those claims. (LLM, conf=0.77)
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Cites
Quantum simulation of the Dirac equation
Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., & Roos, C. F. (2010) · Nature · doi:10.1038/nature08688 · Cited by 725 · see citing works
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Research works printed but not linked: 6
- [1]E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichs¨ ollner, M. Gustavsson, M. Dalmonte, G. Pupillo and H.-C. N¨ agerl, arXiv:1004.3168 (2010). · arXiv
- [3]M. Kormos, G. Mussardo, and A. Trombettoni, Phys. Rev. A 81 , 043606 (2010); L. Lepori, G. Mussardo, A. Trombettoni, arXiv:1004.4744 (2010). · arXiv
- [4]F. L. Semiao, and M. Paternostro, arXiv:1005.2775 (2010). · arXiv
- [5]A. Bermudez, et al. , arXiv:1004.5101 (2010). · arXiv
- [12]W. Thirring, Annals Phys. 3 , 91 (1958).
- [13]V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge Univ. Press, Cambridge (1993).
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Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932 · see citing works
Light-induced gauge fields for ultracold atoms
Goldman, N., Juzeliūnas, G., Öhberg, P., & Spielman, I. B. (2014) · Reports on Progress in Physics · doi:10.1088/0034-4885/77/12/126401 · Cited by 1,212 · see citing works
Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
Lan, Z., Goldman, N., Bermudez, A., Lu, W., & Öhberg, P. (2011) · Physical Review B · doi:10.1103/physrevb.84.165115 · Cited by 119 · see citing works
Relativistic quantum mechanics with trapped ions
Lamata, L., Casanova, J., Gerritsma, R., Roos, C. F., García-Ripoll, J. J., & Solano, E. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/9/095003 · Cited by 80 · see citing works
Classical simulation of relativistic quantum mechanics in periodic optical structures
Longhi, S. (2011) · Applied Physics B · doi:10.1007/s00340-011-4628-7 · Cited by 72 · see citing works
Dirac Cellular Automaton from Split-step Quantum Walk
Mallick, A., & Chandrashekar, C. M. (2016) · Scientific Reports · doi:10.1038/srep25779 · Cited by 45 · see citing works
“ρ ρ = τ τ † t U U ( ) (0)( ) , (33) SQW t SQW t”
- Authors
- Cirac, J. I., Maraner, P., & Pachos, J. K.
- Affiliations
- Max Planck Society (DE)
- Free University of Bozen-Bolzano (IT)
- University of Leeds (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-11-04
- Volume
- 105
- Issue
- 19
- Pages
- 190403-190403
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2038670463
- Cited by
- 157
- References
- 1
- Citations by year
- 2026: 7 · 2025: 6 · 2024: 12 · 2023: 10 · 2022: 4 · 2021: 6 · 2020: 6 · 2019: 7 · 2018: 13 · 2017: 10 · 2016: 8 · 2015: 16 · 2014: 13 · 2013: 13 · 2012: 9
- FWCI
- 6.52
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/E019692/1)
- Topics
- 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 many-body systems
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Keywords
- relativistic quantum field theory, Dirac fermions, Thirring model, Gross-Neveu model, scalar field coupling, two-dimensional field theory, spectral properties, correlation functions
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