Exact solutions of a model for synthetic anyons in a noninteracting system
Open accessAbstract
We study a theoretical model for synthetic anyons in a noninteracting quantum many-body system. Synthetic anyons can occur in a noninteracting system when it is perturbed with specially tailored localized probes, which supply the demanded nontrivial topology in the system. The model is represented by the Hamiltonian for noninteracting electrons in two dimensions, in a uniform magnetic field, pierced with solenoids with a magnetic flux that is a fraction of the flux quantum. In a potential experimental realization of the model, there should be a mechanism fixing the flux in all solenoid probes to an identical value for these perturbations to represent synthetic anyons. We find analytically and numerically the ground state of the model when only the lowest Landau-level states are occupied. We calculate the statistical parameter by using the Berry phase, and show that the ground state is anyonic in the coordinates of the probes. We show that these synthetic anyons cannot be considered as emergent quasiparticles. The fusion rules are discussed for different microscopic realizations of the fusion process.
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As η → 0, the state becomes (2.27), except m is shifted by 1, thus avoiding a spurious divergent state.
“Note that as η → 0 , the state becomes (2.27), except m is shifted by 1 , thus avoiding a spurious divergent state 1 | z | -α exp ( -| z | 2 4 l 2 B ) (see [18]).”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [18]
The Appendix (p. 8) gives the allowed lowest-Landau-level angular quantum numbers as m ≤ −1 for 0 < α < 1 and excludes the divergent m = 0 state as spurious. The available text does not establish the claimed η → 0 limit or its equivalence to the citing paper’s Eq. (2.27), except for a shift in m. (LLM, conf=0.82)
Experimental — accuracy not yet measuredIf one of the pairs is moved in a circle of sufficiently large radius around the other pair, the expected statistical phase is 2 2 × 2π(α - 1).
“For example, if we move one of the pairs in a circle of sufficiently large radius around the other pair, we analytically obtain the expected statistical phase of 2 2 × 2 π ( α -1) (see Appendix B of [18] for details of calculation).”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [18]
For a single probe, the single-particle states of the system at the LLL energy are given by Eq. (4.5).
“For a single probe, the single-particle states of the system at the LLL energy are given by (see Appendix A in [18] for details of the calculation)”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [18]
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Cites
Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas
Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B., & Dalibard, J. (2006) · Nature · doi:10.1038/nature04851 · Cited by 972 · see citing works
Induced Self-Stabilization in Fractional Quantum Hall States of Light
Kapit, E., Hafezi, M., & Simon, S. H. (2014) · Physical Review X · doi:10.1103/physrevx.4.031039 · Cited by 96 · see citing works
Creation and manipulation of anyons in a layered superconductor–two-dimensional electron gas system
Rosenberg, G., Seradjeh, B., Weeks, C., & Franz, M. (2009) · Physical Review B · doi:10.1103/physrevb.79.205102 · Cited by 19 · see citing works
Some Remarks on the Quantum Hall Effect
Pasquier, V. (2013) · Springer Proceedings in Mathematics & Statistics · doi:10.1007/978-1-4471-4863-0_21
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Research works printed but not linked: 2
- [17]M.V. Berry, Proc. R. Soc. Lond. A 392 , 45 (1984).
- [41]E. Jajti´ c, Synthetic magnetism for ultracold atomic gases , Master thesis, University of Zagreb (2018).
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Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems
Lunić, F. (2022) · arXiv · doi:10.48550/arxiv.2208.04270
Self-citation
- Authors
- Lunić, F., Todorić, M., Klajn, B., Dubček, T., Jukić, D., & Buljan, H.
- Affiliations
- University of Zagreb (HR)
- ETH Zurich (CH)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2020-03-20
- Volume
- 101
- Issue
- 11
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2963687609
- Cited by
- 3
- References
- 4
- Citations by year
- 2021: 1 · 2020: 2
- FWCI
- 0.31
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- Hrvatska Zaklada za Znanost (IP-2016-06-5885)
- European Regional Development Fund (KK.01.1.1.01.0004)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- noninteracting electrons, two-dimensional electron gas, uniform magnetic field, solenoid, Berry phase, statistical parameters, ground state, lowest Landau level, fusion rules, anyon statistics
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