- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Letter
  • Open Access

Frustrated magnets without geometrical frustration in bosonic flux ladders

Luca Barbiero1,*, Josep Cabedo2,*,†, Maciej Lewenstein3,4, Leticia Tarruell3,4, and Alessio Celi2

  • 1Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
  • 2Departament de Física, Universitat Autónoma de Barcelona, E-08193 Bellaterra, Spain
  • 3ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avenida Carl Friedrich Gauss 3, E-08860 Castelldefels (Barcelona), Spain
  • 4ICREA, Passeig de Lluís Companys 23, E-08010 Barcelona, Spain

  • *These authors contributed equally to this work.
  • †josep.cabedo@uab.cat
PDF

Phys. Rev. Research 5, L042008 – Published 6 October, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042008

Abstract

We propose a scheme to realize a frustrated Bose-Hubbard model with ultracold atoms in an optical lattice that comprises the frustrated spin-1/2 quantum XX model. Our approach is based on a square ladder of magnetic flux ∼π with one real and one synthetic spin dimension. Although this system does not have geometrical frustration, we show that at low energies it maps into an effective triangular ladder with staggered fluxes for specific values of the synthetic tunneling. We numerically investigate its rich phase diagram and show that it contains bond-ordered-wave and chiral superfluid phases. Our scheme gives access to minimal instances of frustrated magnets without the need for real geometrical frustration, in a setup of minimal experimental complexity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (91)

  1. P. Anderson, Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153 (1973).
  2. L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
  3. C. Lacroix, P. Mendels, and F. Mila, Introduction to Frustrated Magnetism (Springer, Berlin, 2011).
  4. H. T. Diep, Frustrated Spin Systems (World Scientific, Singapore, 2004).
  5. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. Fisher, Deconfined quantum critical points, Science 303, 1490 (2004).
  6. A. W. Sandvik, Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions, Phys. Rev. Lett. 98, 227202 (2007).
  7. S. Jiang and O. Motrunich, Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points, Phys. Rev. B 99, 075103 (2019).
  8. A. Rahmani, A. E. Feiguin, and C. D. Batista, Anyonic liquids in nearly saturated spin chains, Phys. Rev. Lett. 113, 267201 (2014).
  9. C. Majumdar and D. Ghosh, On next-nearest-neighbor interaction in linear chain. I, J. Math. Phys. 10, 1388 (1969).
  10. F. D. M. Haldane, Spontaneous dimerization in the S=12 Heisenberg antiferromagnetic chain with competing interactions, Phys. Rev. B 25, 4925 (1982).
  11. K. Okamoto and K. Nomura, Fluid-dimer critical point in S=1/2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions, Phys. Lett. A 169, 433 (1992).
  12. S. R. White and I. Affleck, Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: Analogies to the Kondo lattice, Phys. Rev. B 54, 9862 (1996).
  13. A. A. Nersesyan, A. O. Gogolin, and F. H. L. Eßler, Incommensurate spin correlations in spin-1/2 frustrated two-leg Heisenberg ladders, Phys. Rev. Lett. 81, 910 (1998).
  14. M. Atala, M. Aidelsburger, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Observation of chiral currents with ultracold atoms in bosonic ladders, Nat. Phys. 10, 588 (2014).
  15. M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, T. Menke, D. Borgnia, P. M. Preiss, F. Grusdt, A. M. Kaufman, and M. Greiner, Microscopy of the interacting Harper–Hofstadter model in the two-body limit, Nature (London) 546, 519 (2017).
  16. A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. Spielman, G. Juzeliūnas, and M. Lewenstein, Synthetic gauge fields in synthetic dimensions, Phys. Rev. Lett. 112, 043001 (2014).
  17. M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science 349, 1510 (2015).
  18. B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, Visualizing edge states with an atomic Bose gas in the quantum Hall regime, Science 349, 1514 (2015).
  19. L. F. Livi, G. Cappellini, M. Diem, L. Franchi, C. Clivati, M. Frittelli, F. Levi, D. Calonico, J. Catani, M. Inguscio, and L. Fallani, Synthetic dimensions and spin-orbit coupling with an optical clock transition, Phys. Rev. Lett. 117, 220401 (2016).
  20. S. Kolkowitz, S. L. Bromley, T. Bothwell, M. L. Wall, G. E. Marti, A. Koller, X. Zhang, A. M. Rey, and J. Ye, Spin–orbit-coupled fermions in an optical lattice clock, Nature (London) 542, 66 (2017).
  21. J. H. Han, J. H. Kang, and Y. Shin, Band gap closing in a synthetic Hall tube of neutral fermions, Phys. Rev. Lett. 122, 065303 (2019).
  22. C.-H. Li, Y. Yan, S.-W. Feng, S. Choudhury, D. B. Blasing, Q. Zhou, and Y. P. Chen, Bose-Einstein condensate on a synthetic topological Hall cylinder, PRX Quantum 3, 010316 (2022).
  23. R. P. Anderson, D. Trypogeorgos, A. Valdés-Curiel, Q.-Y. Liang, J. Tao, M. Zhao, T. Andrijauskas, G. Juzeliūnas, and I. B. Spielman, Realization of a deeply subwavelength adiabatic optical lattice, Phys. Rev. Res. 2, 013149 (2020).
  24. 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, Observation of universal Hall response in strongly interacting Fermions, Science 381, 427 (2023).
  25. S.-L. Drechsler, O. Volkova, A. N. Vasiliev, N. Tristan, J. Richter, M. Schmitt, H. Rosner, J. Málek, R. Klingeler, A. A. Zvyagin, and B. Büchner, Frustrated cuprate route from antiferromagnetic to ferromagnetic spin-12 Heisenberg chains: Li2ZrCuO4 as a missing link near the quantum critical point, Phys. Rev. Lett. 98, 077202 (2007).
  26. C. de Graaf, I. de P. R. Moreira, F. Illas, O. Iglesias, and A. Labarta, Magnetic structure of Li2CuO2: From ab initio calculations to macroscopic simulations, Phys. Rev. B 66, 014448 (2002).
  27. A. U. B. Wolter, F. Lipps, M. Schäpers, S.-L. Drechsler, S. Nishimoto, R. Vogel, V. Kataev, B. Büchner, H. Rosner, M. Schmitt, M. Uhlarz, Y. Skourski, J. Wosnitza, S. Süllow, and K. C. Rule, Magnetic properties and exchange integrals of the frustrated chain cuprate linarite PbCuSO4(OH)2, Phys. Rev. B 85, 014407 (2012).
  28. H.-J. Grafe, S. Nishimoto, M. Iakovleva, E. Vavilova, L. Spillecke, A. Alfonsov, M.-I. Sturza, S. Wurmehl, H. Nojiri, H. Rosner, J. Richter, U. K. Rößler, S.-L. Drechsler, V. Kataev, and B. Büchner, Signatures of a magnetic field-induced unconventional nematic liquid in the frustrated and anisotropic spin-chain cuprate LiCuSbO4, Sci. Rep. 7, 6720 (2017).
  29. A. Orlova, E. L. Green, J. M. Law, D. I. Gorbunov, G. Chanda, S. Krämer, M. Horvatić, R. K. Kremer, J. Wosnitza, and G. L. J. A. Rikken, Nuclear magnetic resonance signature of the spin-nematic phase in LiCuVO4 at high magnetic fields, Phys. Rev. Lett. 118, 247201 (2017).
  30. H. Ueda, S. Onoda, Y. Yamaguchi, T. Kimura, D. Yoshizawa, T. Morioka, M. Hagiwara, M. Hagihala, M. Soda, T. Masuda, T. Sakakibara, K. Tomiyasu, S. Ohira-Kawamura, K. Nakajima, R. Kajimoto, M. Nakamura, Y. Inamura, N. Reynolds, M. Frontzek, J. S. White et al., Emergent spin-1 Haldane gap and ferroelectricity in a frustrated spin-12 ladder, Phys. Rev. B 101, 140408 (2020).
  31. C. P. Grams, D. Brüning, S. Kopatz, T. Lorenz, P. Becker, L. Bohatý, and J. Hemberger, Observation of chiral solitons in LiCuVO4, Commun. Phys. 5, 37 (2022).
  32. L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature (London) 483, 302 (2012).
  33. J. Yang, L. Liu, J. Mongkolkiattichai, and P. Schauss, Site-resolved imaging of ultracold fermions in a triangular-lattice quantum gas microscope, PRX Quantum 2, 020344 (2021).
  34. Z. Z. Yan, B. M. Spar, M. L. Prichard, S. Chi, H.-T. Wei, E. Ibarra-García-Padilla, K. R. A. Hazzard, and W. S. Bakr, Two-dimensional programmable tweezer arrays of fermions, Phys. Rev. Lett. 129, 123201 (2022).
  35. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom Fermi–Hubbard antiferromagnet, Nature (London) 545, 462 (2017).
  36. J. Mongkolkiattichai, L. Liu, D. Garwood, J. Yang, and P. Schauss, Quantum gas microscopy of a geometrically frustrated Hubbard system, arXiv:2210.14895.
  37. A. Eckardt, P. Hauke, P. Soltan-Panahi, C. Becker, K. Sengstock, and M. Lewenstein, Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice, Europhys. Lett. 89, 10010 (2010).
  38. A. Celi, T. Grass, A. J. Ferris, B. Padhi, D. Raventós, J. Simonet, K. Sengstock, and M. Lewenstein, Modified spin-wave theory and spin-liquid behavior of cold bosons on an inhomogeneous triangular lattice, Phys. Rev. B 94, 075110 (2016).
  39. J. Struck, C. Ölschläger, R. Le Targat, P. Soltan-Panahi, A. Eckardt, M. Lewenstein, P. Windpassinger, and K. Sengstock, Quantum simulation of frustrated classical magnetism in triangular optical lattices, Science 333, 996 (2011).
  40. J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields, Nat. Phys. 9, 738 (2013).
  41. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, Experimental realization of strong effective magnetic fields in an optical lattice, Phys. Rev. Lett. 107, 255301 (2011).
  42. M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett. 111, 185301 (2013).
  43. H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices, Phys. Rev. Lett. 111, 185302 (2013).
  44. C. Weitenberg and J. Simonet, Tailoring quantum gases by Floquet engineering, Nat. Phys. 17, 1342 (2021).
  45. O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, Quantum simulation of an extra dimension, Phys. Rev. Lett. 108, 133001 (2012).
  46. E. Anisimovas, M. Račiūnas, C. Sträter, A. Eckardt, I. B. Spielman, and G. Juzeliūnas, Semisynthetic zigzag optical lattice for ultracold bosons, Phys. Rev. A 94, 063632 (2016).
  47. D. Suszalski and J. Zakrzewski, Different lattice geometries with a synthetic dimension, Phys. Rev. A 94, 033602 (2016).
  48. J. Cabedo, J. Claramunt, J. Mompart, V. Ahufinger, and A. Celi, Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices, Eur. Phys. J. D 74, 123 (2020).
  49. M. Mamaev, I. Kimchi, R. M. Nandkishore, and A. M. Rey, Tunable-spin-model generation with spin-orbit-coupled fermions in optical lattices, Phys. Rev. Res. 3, 013178 (2021).
  50. M. Mamaev, T. Bilitewski, B. Sundar, and A. M. Rey, Resonant dynamics of strongly interacting SU(n) fermionic atoms in a synthetic flux ladder, PRX Quantum 3, 030328 (2022).
  51. M. Sato, S. Furukawa, S. Onoda, and A. Furusaki, Competing phases in spin-1/2J1−J2 chain with easy-plane anisotropy, Mod. Phys. Lett. B 25, 901 (2011).
  52. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L042008 for a detailed derivation of the lower-band model, a discussion of its symmetry-broken phases and meaningful observables, and of the experimental viability of our proposal, which includes Refs. [53, 54, 55, 56, 57, 58, 59, 60].
  53. Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature (London) 471, 83 (2011).
  54. C. K. Majumdar, Antiferromagnetic model with known ground state, J. Phys. C: Solid State Phys. 3, 911 (1970).
  55. S. Greschner, M. Piraud, F. Heidrich-Meisner, I. P. McCulloch, U. Schollwöck, and T. Vekua, Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: Swimming against the tide, Phys. Rev. Lett. 115, 190402 (2015).
  56. M. Di Dio, S. De Palo, E. Orignac, R. Citro, and M.-L. Chiofalo, Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux, Phys. Rev. B 92, 060506 (2015).
  57. A. Frölian, Simulating a topological gauge theory in a Raman-dressed Bose-Einstein condensate, Ph.D. thesis, Universitat Politècnica de Catalunya, 2022, http://hdl.handle.net/2117/367335.
  58. R. Wei and E. J. Mueller, Magnetic-field dependence of Raman coupling in alkali-metal atoms, Phys. Rev. A 87, 042514 (2013).
  59. A. Frölian, C. S. Chisholm, E. Neri, C. R. Cabrera, R. Ramos, A. Celi, and L. Tarruell, Realizing a 1D topological gauge theory in an optically dressed BEC, Nature (London) 608, 293 (2022).
  60. D. Wei, A. Rubio-Abadal, B. Ye, F. Machado, J. Kemp, K. Srakaew, S. Hollerith, J. Rui, S. Gopalakrishnan, N. Y. Yao, I. Bloch, and J. Zeiher, Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion, Science 376, 716 (2022).
  61. S. Greschner, L. Santos, and T. Vekua, Ultracold bosons in zig-zag optical lattices, Phys. Rev. A 87, 033609 (2013).
  62. M. P. Zaletel, S. A. Parameswaran, A. Rüegg, and E. Altman, Chiral bosonic Mott insulator on the frustrated triangular lattice, Phys. Rev. B 89, 155142 (2014).
  63. C. Romen and A. M. Läuchli, Chiral Mott insulators in frustrated Bose-Hubbard models on ladders and two-dimensional lattices: A combined perturbative and density matrix renormalization group study, Phys. Rev. B 98, 054519 (2018).
  64. S. Greschner and T. Mishra, Interacting bosons in generalized zigzag and railroad-trestle models, Phys. Rev. B 100, 144405 (2019).
  65. C.-M. Halati and T. Giamarchi, Bose-Hubbard triangular ladder in an artificial gauge field, Phys. Rev. Res. 5, 013126 (2023).
  66. T. Mishra, R. V. Pai, S. Mukerjee, and A. Paramekanti, Quantum phases and phase transitions of frustrated hard-core bosons on a triangular ladder, Phys. Rev. B 87, 174504 (2013).
  67. T. Mishra, R. V. Pai, and S. Mukerjee, Supersolid in a one-dimensional model of hard-core bosons, Phys. Rev. A 89, 013615 (2014).
  68. E. Orignac and T. Giamarchi, Meissner effect in a bosonic ladder, Phys. Rev. B 64, 144515 (2001).
  69. R. Wei and E. J. Mueller, Theory of bosons in two-leg ladders with large magnetic fields, Phys. Rev. A 89, 063617 (2014).
  70. A. Tokuno and A. Georges, Ground states of a Bose–Hubbard ladder in an artificial magnetic field: Field-theoretical approach, New J. Phys. 16, 073005 (2014).
  71. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  72. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  73. M. Piraud, F. Heidrich-Meisner, I. P. McCulloch, S. Greschner, T. Vekua, and U. Schollwöck, Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder, Phys. Rev. B 91, 140406 (2015).
  74. S. Greschner, M. Piraud, F. Heidrich-Meisner, I. P. McCulloch, U. Schollwöck, and T. Vekua, Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field, Phys. Rev. A 94, 063628 (2016).
  75. A. Petrescu and K. Le Hur, Bosonic Mott insulator with Meissner currents, Phys. Rev. Lett. 111, 150601 (2013).
  76. M. Buser, C. Hubig, U. Schollwöck, L. Tarruell, and F. Heidrich-Meisner, Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics, Phys. Rev. A 102, 053314 (2020).
  77. D. Trypogeorgos, A. Valdés-Curiel, N. Lundblad, and I. B. Spielman, Synthetic clock transitions via continuous dynamical decoupling, Phys. Rev. A 97, 013407 (2018).
  78. R. P. Anderson, M. J. Kewming, and L. D. Turner, Continuously observing a dynamically decoupled spin-1 quantum gas, Phys. Rev. A 97, 013408 (2018).
  79. X.-Q. Wang, G.-Q. Luo, J.-Y. Liu, G.-H. Huang, Z.-X. Li, C. Wu, A. Hemmerich, and Z.-F. Xu, Observation of nematic orbital superfluidity in a triangular optical lattice, arXiv:2211.05578.
  80. S. Singha Roy, L. Carl, and P. Hauke, Genuine multipartite entanglement in a one-dimensional Bose-Hubbard model with frustrated hopping, Phys. Rev. B 106, 195158 (2022).
  81. M. Buser, F. Heidrich-Meisner, and U. Schollwöck, Finite-temperature properties of interacting bosons on a two-leg flux ladder, Phys. Rev. A 99, 053601 (2019).
  82. S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms, Science 365, 775 (2019).
  83. V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de Léséleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. Büchler, T. Lahaye, and A. Browaeys, Realization of a density-dependent peierls phase in a synthetic, spin-orbit coupled Rydberg system, Phys. Rev. X 10, 021031 (2020).
  84. T. Graß, C. Muschik, A. Celi, R. W. Chhajlany, and M. Lewenstein, Synthetic magnetic fluxes and topological order in one-dimensional spin systems, Phys. Rev. A 91, 063612 (2015).
  85. Y. Shapira, T. Manovitz, N. Akerman, A. Stern, and R. Ozeri, Quantum simulations of interacting systems with broken time-reversal symmetry, arXiv:2205.11178v1.
  86. A. V. Gorshkov, S. R. Manmana, G. Chen, J. Ye, E. Demler, M. D. Lukin, and A. M. Rey, Tunable superfluidity and quantum magnetism with ultracold polar molecules, Phys. Rev. Lett. 107, 115301 (2011).
  87. J. L. Bohn, A. M. Rey, and J. Ye, Cold molecules: Progress in quantum engineering of chemistry and quantum matter, Science 357, 1002 (2017).
  88. J. S. Douglas, H. Habibian, C.-L. Hung, A. V. Gorshkov, H. J. Kimble, and D. E. Chang, Quantum many-body models with cold atoms coupled to photonic crystals, Nat. Photon. 9, 326 (2015).
  89. D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, Colloquium: Quantum matter built from nanoscopic lattices of atoms and photons, Rev. Mod. Phys. 90, 031002 (2018).
  90. E. Colella, A. Kosior, F. Mivehvar, and H. Ritsch, Open quantum system simulation of faraday's induction law via dynamical instabilities, Phys. Rev. Lett. 128, 070603 (2022).
  91. M. Di Liberto and N. Goldman, Chiral orbital order of interacting bosons without higher bands, Phys. Rev. Res. 5, 023064 (2023).

Outline

Information

Phys. Rev. Research 5, L042008– Published 6 October, 2023
  • Received 22 December 2022
  • Revised 7 August 2023
  • Accepted 14 September 2023
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