Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model
Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/acb963 |
| _version_ | 1797748757335375872 |
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| author | F A Palm M Kurttutan A Bohrdt U Schollwöck F Grusdt |
| author_facet | F A Palm M Kurttutan A Bohrdt U Schollwöck F Grusdt |
| author_sort | F A Palm |
| collection | DOAJ |
| description | Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν = 1. We reveal the nature of the low energy spin-singlet states around ν ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- $T_\mathrm{c}$ superconductivity. |
| first_indexed | 2024-03-12T16:09:24Z |
| format | Article |
| id | doaj.art-5204102f2aec42abb6f4c971cc1b8ff1 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:09:24Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-5204102f2aec42abb6f4c971cc1b8ff12023-08-09T14:11:35ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125202302110.1088/1367-2630/acb963Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard modelF A Palm0https://orcid.org/0000-0001-5774-5546M Kurttutan1A Bohrdt2https://orcid.org/0000-0002-3339-5200U Schollwöck3https://orcid.org/0000-0002-2538-1802F Grusdt4https://orcid.org/0000-0003-3531-8089Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC) , Ludwig-Maximilians-Universität München, Theresienstr. 37, D-80333 München, Germany; Munich Center for Quantum Science and Technology (MCQST) , Schellingstr. 4, D-80799 München, GermanyDepartment of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC) , Ludwig-Maximilians-Universität München, Theresienstr. 37, D-80333 München, Germany; Munich Center for Quantum Science and Technology (MCQST) , Schellingstr. 4, D-80799 München, Germany; Department of Physics, Freie Universität Berlin , Arnimallee 14, D-14195 Berlin, GermanyDepartment of Physics, Harvard University , Cambridge, MA 02138, United States of America; ITAMP, Harvard-Smithsonian Center for Astrophysics , Cambridge, MA 02138, United States of AmericaDepartment of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC) , Ludwig-Maximilians-Universität München, Theresienstr. 37, D-80333 München, Germany; Munich Center for Quantum Science and Technology (MCQST) , Schellingstr. 4, D-80799 München, GermanyDepartment of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC) , Ludwig-Maximilians-Universität München, Theresienstr. 37, D-80333 München, Germany; Munich Center for Quantum Science and Technology (MCQST) , Schellingstr. 4, D-80799 München, GermanyStrongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν = 1. We reveal the nature of the low energy spin-singlet states around ν ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- $T_\mathrm{c}$ superconductivity.https://doi.org/10.1088/1367-2630/acb963ultracold atomsskyrmionsquantum Hall effectquantum Hall ferromagnetoptical lattices |
| spellingShingle | F A Palm M Kurttutan A Bohrdt U Schollwöck F Grusdt Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model New Journal of Physics ultracold atoms skyrmions quantum Hall effect quantum Hall ferromagnet optical lattices |
| title | Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model |
| title_full | Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model |
| title_fullStr | Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model |
| title_full_unstemmed | Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model |
| title_short | Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model |
| title_sort | ferromagnetism and skyrmions in the hofstadter fermi hubbard model |
| topic | ultracold atoms skyrmions quantum Hall effect quantum Hall ferromagnet optical lattices |
| url | https://doi.org/10.1088/1367-2630/acb963 |
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