- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Flux Magnetism in a Strongly Interacting Dipolar Lattice Supersolid under Tunable Gauge Fields

Michele Miotto1,*, Pietro Lombardi2,3, Giovanni Ferioli4, Joana Fraxanet5, Maciej Lewenstein5,6, Luca Tanzi2,3, and Luca Barbiero7,†

  • *Contact author: m.miotto@tu-berlin.de
  • †Contact author: luca.barbiero@polito.it
PDF

Phys. Rev. Lett. 137, 043401 – Published 22 July, 2026

DOI: https://doi.org/10.1103/tbp3-7rh3

Abstract

Supersolidity and magnetism are fundamental phenomena characterizing strongly correlated matter. Here we unveil a mechanism that directly connects these two regimes and can be experimentally accessed in ultracold atomic systems. Specifically, we exploit the distinctive properties of magnetic lanthanide atoms trapped in a one-dimensional antimagic wavelength optical lattice. This platform enables a realistic implementation of a triangular Bose-Hubbard ladder featuring two key ingredients: strong long-range interactions and tunable gauge fields. Owing to these properties, our numerical analysis reveals a robust lattice supersolid regime with finite fluxes in each triangular plaquette. Remarkably, we show that the density modulation of the supersolid phase and a finite gauge field induce magnetic ordering of the fluxes, forming ferromagnetic and ferrimagnetic patterns. Our results thus reveal a quantum effect that bridges supersolidity and magnetism.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (99)

  1. D. J. Thouless, The Quantum Mechanics of Many-Body Systems (Courier Corporation, Mineola, NY, 2013).
  2. S. M. Girvin and K. Yang, Modern Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2019).
  3. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), and U. Sen, Adv. Phys. 56, 243 (2007).
  4. M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford University Press, Oxford, 2012).
  5. C. Gross and I. Bloch, Science 357, 995 (2017).
  6. N. Goldman, J. C. Budich, and P. Zoller, Nat. Phys. 12, 639 (2016).
  7. J. Argüello-Luengo, A. González-Tudela, T. Shi, P. Zoller, and J. I. Cirac, Nature (London) 574, 215 (2019).
  8. D.-W. Zhang, Y.-Q. Zhu, Y. X. Zhao, H. Yan, and S.-L. Zhu, Adv. Phys. 67, 253 (2018).
  9. M. Aidelsburger et al., Phil. Trans. R. Soc. A 380, 20210064 (2022).
  10. K. H. J. Buschow and F. R. de Boer, Physics of Magnetism and Magnetic Materials, Focus on Biotechnology (Springer US, New York, 2003).
  11. A. Auerbach, Interacting Electrons and Quantum Magnetism, Graduate Texts in Contemporary Physics (Springer, New York, 2012).
  12. C. V. Parker, L.-C. Ha, and C. Chin, Nat. Phys. 9, 769 (2013).
  13. R. Cominotti, A. Berti, C. Dulin, C. Rogora, G. Lamporesi, I. Carusotto, A. Recati, A. Zenesini, and G. Ferrari, Phys. Rev. X 13, 021037 (2023).
  14. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, Nature (London) 545, 462 (2017).
  15. H.-J. Shao, Y.-X. Wang, D.-Z. Zhu, Y.-S. Zhu, H.-N. Sun, S.-Y. Chen, C. Zhang, Z.-J. Fan, Y. Deng, X.-C. Yao et al., Nature (London) 632, 267 (2024).
  16. M. Lebrat, A. Kale, L. H. Kendrick, M. Xu, Y. Gang, A. Nikolaenko, P. M. Bonetti, S. Sachdev, and M. Greiner, Science 392, 612 (2026).
  17. K. Góral, L. Santos, and M. Lewenstein, Phys. Rev. Lett. 88, 170406 (2002).
  18. A. Recati and S. Stringari, Nat. Rev. Phys. 5, 735 (2023).
  19. A. F. Andreev and I. M. Lifshitz, Sov. Phys. JETP 29, 1107 (1969), http://www.jetp.ras.ru/cgi-bin/e/index/e/29/6/p1107?a=list.
  20. G. V. Chester, Phys. Rev. A 2, 256 (1970).
  21. A. J. Leggett, Phys. Rev. Lett. 25, 1543 (1970).
  22. J.-R. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F. Ç. Top, A. O. Jamison, and W. Ketterle, Nature (London) 543, 91 (2017).
  23. J. Léonard, A. Morales, P. Zupancic, T. Esslinger, and T. Donner, Nature (London) 543, 87 (2017).
  24. C. S. Chisholm, S. Hirthe, V. B. Makhalov, R. Ramos, R. Vatré, J. Cabedo, A. Celi, and L. Tarruell, Science 391, 480 (2026).
  25. L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe-Tolra, B. L. Lev, and T. Pfau, Rep. Prog. Phys. 86, 026401 (2022).
  26. L. Tanzi, S. M. Roccuzzo, E. Lucioni, F. Famà, A. Fioretti, C. Gabbanini, G. Modugno, A. Recati, and S. Stringari, Nature (London) 574, 382 (2019).
  27. M. Guo, F. Böttcher, J. Hertkorn, J.-N. Schmidt, M. Wenzel, H. P. Büchler, T. Langen, and T. Pfau, Nature (London) 574, 386 (2019).
  28. L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. M. W. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, and F. Ferlaino, Phys. Rev. X 9, 021012 (2019).
  29. A. de Paz, A. Sharma, A. Chotia, E. Maréchal, J. H. Huckans, P. Pedri, L. Santos, O. Gorceix, L. Vernac, and B. Laburthe-Tolra, Phys. Rev. Lett. 111, 185305 (2013).
  30. S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Science 352, 201 (2016).
  31. S. Lepoutre, J. Schachenmayer, L. Gabardos, B. Zhu, B. Naylor, E. Maréchal, O. Gorceix, A. M. Rey, L. Vernac, and B. Laburthe-Tolra, Nat. Commun. 10, 1714 (2019).
  32. A. Patscheider, B. Zhu, L. Chomaz, D. Petter, S. Baier, A.-M. Rey, F. Ferlaino, and M. J. Mark, Phys. Rev. Res. 2, 023050 (2020).
  33. L. Su, A. Douglas, M. Szurek, R. Groth, S. F. Ozturk, A. Krahn, A. H. Hébert, G. A. Phelps, S. Ebadi, S. Dickerson, F. Ferlaino, O. Marković, and M. Greiner, Nature (London) 622, 724 (2023).
  34. L. Du, P. Barral, M. Cantara, J. de Hond, Y.-K. Lu, and W. Ketterle, Science 384, 546 (2024).
  35. Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Nature (London) 471, 83 (2011).
  36. A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzelūnas, and M. Lewenstein, Phys. Rev. Lett. 112, 043001 (2014).
  37. M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, Science 349, 1510 (2015).
  38. B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, Science 349, 1514 (2015).
  39. J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, Nat. Phys. 9, 738 (2013).
  40. E. Anisimovas, M. Račiūnas, C. Sträter, A. Eckardt, I. B. Spielman, and G. Juzeliūnas, Phys. Rev. A 94, 063632 (2016).
  41. C.-M. Halati and T. Giamarchi, Phys. Rev. Res. 5, 013126 (2023).
  42. N. Baldelli, C. R. Cabrera, S. Julià-Farré, M. Aidelsburger, and L. Barbiero, Phys. Rev. Lett. 132, 153401 (2024).
  43. T. Chanda, L. Barbiero, M. Lewenstein, M. J. Mark, and J. Zakrzewski, Rep. Prog. Phys. 88, 044501 (2025).
  44. Y. Li, H. Cai, D. W. Wang, L. Li, J. Yuan, and W. Li, Phys. Rev. Lett. 124, 140401 (2020).
  45. G. G. Batrouni, R. T. Scalettar, V. G. Rousseau, and B. Grémaud, Phys. Rev. Lett. 110, 265303 (2013).
  46. Y. Li, L. He, and W. Hofstetter, Phys. Rev. A 87, 051604 (2013).
  47. T. Mishra, S. Greschner, and L. Santos, Phys. Rev. A 91, 043614 (2015).
  48. R. Kraus, T. Chanda, J. Zakrzewski, and G. Morigi, Phys. Rev. B 106, 035144 (2022).
  49. H. Li, J.-F. Wyart, O. Dulieu, S. Nascimbène, and M. Lepers, J. Phys. B 50, 014005 (2017).
  50. J. H. Becher, S. Baier, K. Aikawa, M. Lepers, J.-F. Wyart, O. Dulieu, and F. Ferlaino, Phys. Rev. A 97, 012509 (2018).
  51. T. Chalopin, V. Makhalov, C. Bouazza, A. Evrard, A. Barker, M. Lepers, J.-F. Wyart, O. Dulieu, J. Dalibard, R. Lopes, and S. Nascimbene, Phys. Rev. A 98, 040502(R) (2018).
  52. D. Bloch, B. Hofer, S. R. Cohen, A. Browaeys, and I. Ferrier-Barbut, Phys. Rev. Lett. 131, 203401 (2023).
  53. See Supplemental Material http://link.aps.org/supplemental/10.1103/tbp3-7rh3 for a precise derivation of the antimagic optical lattice condition, tunability of the Hamiltonian parameters, the detection schemes for the quantities defined in the text, characterization of the chiral superfluid phase, and calculation of the flux patterns. The Supplemental Material includes Refs. [54–59].
  54. M. Lepers, J.-F. Wyart, and O. Dulieu, Phys. Rev. A 89, 022505 (2014).
  55. V. A. Dzuba, V. V. Flambaum, and B. L. Lev, Phys. Rev. A 83, 032502 (2011).
  56. D. Bloch, B. Hofer, S. R. Cohen, M. Lepers, A. Browaeys, and I. Ferrier-Barbut, Phys. Rev. A 110, 033103 (2024).
  57. B. Pasquiou, E. Maréchal, G. Bismut, P. Pedri, L. Vernac, O. Gorceix, and B. Laburthe-Tolra, Phys. Rev. Lett. 106, 255303 (2011).
  58. N. Q. Burdick, K. Baumann, Y. Tang, M. Lu, and B. L. Lev, Phys. Rev. Lett. 114, 023201 (2015).
  59. M. Gall, N. Wurz, J. Samland, C. F. Chan, and M. Köhl, Nature (London) 589, 40 (2021).
  60. M. Sohmen, M. J. Mark, M. Greiner, and F. Ferlaino, SciPost Phys. 15, 182 (2023).
  61. J. Fraxanet, D. González-Cuadra, T. Pfau, M. Lewenstein, T. Langen, and L. Barbiero, Phys. Rev. Lett. 128, 043402 (2022).
  62. M. Lecomte, A. Journeaux, J. Veschambre, J. Dalibard, and R. Lopes, Phys. Rev. Lett. 134, 013402 (2025).
  63. L. Christakis, J. S. Rosenberg, R. Raj, S. Chi, A. Morningstar, D. A. Huse, Z. Z. Yan, and W. S. Bakr, Nature (London) 614, 64 (2023).
  64. A. N. Carroll, H. Hirzler, C. Miller, D. Wellnitz, S. R. Muleady, J. Lin, K. P. Zamarski, R. R. W. Wang, J. L. Bohn, A. M. Rey, and J. Ye, Science 388, 381 (2025).
  65. N. Q. Burdick, Y. Tang, and B. L. Lev, Phys. Rev. X 6, 031022 (2016).
  66. S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
  67. U. Schollwöck, Ann. Phys. (Amsterdam) 326, 96 (2011).
  68. J. Hauschild et al., SciPost Phys. Codebases 41 (2024).
  69. A. Eckardt, P. Hauke, P. Soltan-Panahi, C. Becker, K. Sengstock, and M. Lewenstein, Europhys. Lett. 89, 10010 (2010).
  70. J. Cabedo, J. Claramunt, J. Mompart, V. Ahufinger, and A. Celi, Eur. Phys. J. D 74, 123 (2020).
  71. S. Singha Roy, L. Carl, and P. Hauke, Phys. Rev. B 106, 195158 (2022).
  72. L. Barbiero, J. Cabedo, M. Lewenstein, L. Tarruell, and A. Celi, Phys. Rev. Res. 5, L042008 (2023).
  73. C.-M. Halati and T. Giamarchi, Phys. Rev. Res. 7, 013199 (2025).
  74. D. Burba, G. Juzeliūnas, I. B. Spielman, and L. Barbiero, Commun. Phys. 8, 141 (2025).
  75. E. G. Dalla Torre, E. Berg, and E. Altman, Phys. Rev. Lett. 97, 260401 (2006).
  76. X. Deng and L. Santos, Phys. Rev. B 84, 085138 (2011).
  77. D. Rossini and R. Fazio, New J. Phys. 14, 065012 (2012).
  78. S. Ejima and H. Fehske, Phys. Rev. B 91, 045121 (2015).
  79. K. Kottmann, P. Huembeli, M. Lewenstein, and A. Acín, Phys. Rev. Lett. 125, 170603 (2020).
  80. E. Berg, E. G. Dalla Torre, T. Giamarchi, and E. Altman, Phys. Rev. B 77, 245119 (2008).
  81. M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M. C. Bañuls, L. Pollet, I. Bloch, and S. Kuhr, Science 334, 200 (2011).
  82. A. Dhar, M. Maji, T. Mishra, R. V. Pai, S. Mukerjee, and A. Paramekanti, Phys. Rev. A 85, 041602 (2012).
  83. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, New York, 2004).
  84. T. D. Kühner, S. R. White, and H. Monien, Phys. Rev. B 61, 12474 (2000).
  85. W. Han, X.-F. Zhang, D.-S. Wang, H.-F. Jiang, W. Zhang, and S.-G. Zhang, Phys. Rev. Lett. 121, 030404 (2018).
  86. O. M. Yevtushenko and A. M. Tsvelik, Phys. Rev. B 98, 081118 (2018).

  87. For a triangular ladder with L sites, the sum of △ and ▽ plaquettes is L−2. Furthermore, the ground state of the lattice SS phase is twofold degenerate, reflecting the equal probability of having high occupations in even or odd sites. Since we chose L to be odd in order to lift this degeneracy, we exclude a plaquette in the calculation: this allows us to consider the same number of △ and ▽ plaquettes, thus justifying the factor L−3 in Eq. (7).

  88. Here we find only S(k=0)≠0, consistent with a homogeneous superfluid.

  89. M. Piraud, F. Heidrich-Meisner, I. P. McCulloch, S. Greschner, T. Vekua, and U. Schollwöck, Phys. Rev. B 91, 140406 (2015).
  90. A. Impertro, S. Huh, S. Karch, J. F. Wienand, I. Bloch, and M. Aidelsburger, Nat. Phys. 21, 895 (2025).

  91. In the text we selected the configuration favoring high occupation in odd sites, while the opposite one would imply |jm△→|<|jm▽→| and therefore |Φm△→|<|Φm▽→|.

  92. M. Greiner, O. Mandel, T. Esslinger, T. Hänsch, and I. Bloch, Nature (London) 415, 39 (2002).
  93. A. Impertro, S. Karch, J. F. Wienand, S. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Phys. Rev. Lett. 133, 063401 (2024).
  94. T.-W. Zhou, G. Cappellini, D. Tusi, L. Franchi, J. Parravicini, C. Repellin, S. Greschner, M. Inguscio, T. Giamarchi, M. Filippone, J. Catani, and L. Fallani, Science 381, 427 (2023).
  95. F. Claude, L. Lafforgue, J. J. A. Houwman, M. J. Mark, and F. Ferlaino, Phys. Rev. Res. 6, L042016 (2024).
  96. A. Douglas, V. Kaxiras, L. Su, M. Szurek, V. Singh, O. Marković, and M. Greiner, Phys. Rev. X 15, 041021 (2025).
  97. B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, and G. Pupillo, Phys. Rev. Lett. 104, 125301 (2010).
  98. G. Giuliani and G. Vignale, Meaning of the highest occupied Kohn–Sham eigenvalue in metals, in Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, England, 2005), pp. 717–718.
  99. M. Miotto, P. Lombardi, G. Ferioli, J. Fraxanet, M. Lewenstein, L. Tanzi, and L. Barbiero, Flux magnetism in a strongly interacting dipolar lattice supersolid under tunable gauge fields, (1.0) [Data set], Zenodo, 10.5281/zenodo.20848635 (2026).

Outline

Information

Phys. Rev. Lett. 137, 043401– Published 22 July, 2026
  • Received 19 September 2025
  • Revised 10 June 2026
  • Accepted 12 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation