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Topological quantum floating phase of dipolar bosons in an optical ladder
Phys. Rev. A 112, L011301 – Published 1 July, 2025
DOI: https://doi.org/10.1103/lhfx-c4xr
Abstract
Ultracold dipolar hard-core bosons in optical ladders provide exciting possibilities for the quantum simulation of anisotropic spin ladders. We show that introducing a tilt along the rungs results in a rich phase diagram at unit rung filling. In particular, for a sufficiently strong dipolar strength, the interplay between the long-range tail of the dipolar interactions and the tilting leads to the emergence of a quantum floating phase, a critical phase with incommensurate density-density correlations. Interestingly, the floating phase is topological, constituting an intermediate gapless stage in the melting of a crystal into a gapped topological Haldane phase. This novel scenario for topological floating phases in dipolar spin ladders can be investigated in ongoing experiments.
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References (54)
- I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
- S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch, Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices, Science 319, 295 (2008).
- 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).
- A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
- E. Dagotto and T. M. Rice, Surprises on the way from one- to two-dimensional quantum magnets: The ladder materials, Science 271, 618 (1996).
- E. Dagotto, Experiments on ladders reveal a complex interplay between a spin-gapped normal state and superconductivity, Rep. Prog. Phys. 62, 1525 (1999).
- H.-J. Mikeska and A. K. Kolezhuk, One-dimensional magnetism, in Quantum Magnetism, edited by U. Schollwöck, J. Richter, D. J. J. Farnell, and R. F. Bishop (Springer, Berlin, Heidelberg, 2004), pp. 1–83.
- K. Hijii, A. Kitazawa, and K. Nomura, Phase diagram of two-leg spin-ladder systems, Phys. Rev. B 72, 014449 (2005).
- S.-H. Li, Q.-Q. Shi, M. T. Batchelor, and H.-Q. Zhou, Groundstate fidelity phase diagram of the fully anisotropic two-leg spin- XXZ ladder, New J. Phys. 19, 113027 (2017).
- R. Steinigeweg, F. Heidrich-Meisner, J. Gemmer, K. Michielsen, and H. De Raedt, Scaling of diffusion constants in the spin- XX ladder, Phys. Rev. B 90, 094417 (2014).
- D. Schubert, J. Richter, F. Jin, K. Michielsen, H. De Raedt, and R. Steinigeweg, Quantum versus classical dynamics in spin models: Chains, ladders, and square lattices, Phys. Rev. B 104, 054415 (2021).
- T. Rakovszky, C. W. von Keyserlingk, and F. Pollmann, Dissipation-assisted operator evolution method for capturing hydrodynamic transport, Phys. Rev. B 105, 075131 (2022).
- G. A. Domínguez-Castro, T. Bilitewski, D. Wellnitz, A. M. Rey, and L. Santos, Relaxation in dipolar spin ladders: From pair production to false-vacuum decay, Phys. Rev. A 110, L021302 (2024).
- P. Sompet, S. Hirthe, D. Bourgund, T. Chalopin, J. Bibo, J. Koepsell, P. Bojović, R. Verresen, F. Pollmann, G. Salomon, C. Gross, T. A. Hilker, and I. Bloch, Realizing the symmetry-protected Haldane phase in Fermi–Hubbard ladders, Nature (London) 606, 484 (2022).
- J. F. Wienand, S. Karch, A. Impertro, C. Schweizer, E. McCulloch, R. Vasseur, S. Gopalakrishnan, M. Aidelsburger, and I. Bloch, Emergence of fluctuating hydrodynamics in chaotic quantum systems, Nat. Phys. 20, 1732 (2024).
- A. de Paz, A. Sharma, A. Chotia, E. Maréchal, J. H. Huckans, P. Pedri, L. Santos, O. Gorceix, L. Vernac, and B. Laburthe-Tolra, Nonequilibrium quantum magnetism in a dipolar lattice gas, Phys. Rev. Lett. 111, 185305 (2013).
- S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Extended Bose-Hubbard models with ultracold magnetic atoms, Science 352, 201 (2016).
- P. Fersterer, A. Safavi-Naini, B. Zhu, L. Gabardos, S. Lepoutre, L. Vernac, B. Laburthe-Tolra, P. B. Blakie, and A. M. Rey, Dynamics of an itinerant spin-3 atomic dipolar gas in an optical lattice, Phys. Rev. A 100, 033609 (2019).
- 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, Dipolar quantum solids emerging in a Hubbard quantum simulator, Nature (London) 622, 724 (2023).
- B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Observation of dipolar spin-exchange interactions with lattice-confined polar molecules, Nature (London) 501, 521 (2013).
- L. Christakis, J. S. Rosenberg, R. Raj, S. Chi, A. Morningstar, D. A. Huse, Z. Z. Yan, and W. S. Bakr, Probing site-resolved correlations in a spin system of ultracold molecules, Nature (London) 614, 64 (2023).
- C. M. Holland, Y. Lu, and L. W. Cheuk, On-demand entanglement of molecules in a reconfigurable optical tweezer array, Science 382, 1143 (2023).
- Y. Bao, S. S. Yu, L. Anderegg, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Dipolar spin-exchange and entanglement between molecules in an optical tweezer array, Science 382, 1138 (2023).
- 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, Observation of generalized t-J spin dynamics with tunable dipolar interactions, Science 388, 381 (2025).
- 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).
- 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).
- A. Signoles, T. Franz, R. Ferracini Alves, M. Gärttner, S. Whitlock, G. Zürn, and M. Weidemüller, Glassy dynamics in a disordered Heisenberg quantum spin system, Phys. Rev. X 11, 011011 (2021).
- P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Zürn, T. Lahaye, M. Weidemüller, and A. Browaeys, Microwave engineering of programmable Hamiltonians in arrays of Rydberg atoms, PRX Quantum 3, 020303 (2022).
- G. Bornet, G. Emperauger, C. Chen, B. Ye, M. Block, M. Bintz, J. A. Boyd, D. Barredo, T. Comparin, F. Mezzacapo, T. Roscilde, T. Lahaye, N. Y. Yao, and A. Browaeys, Scalable spin squeezing in a dipolar Rydberg atom array, Nature (London) 621, 728 (2023).
- T. Chanda, L. Barbiero, M. Lewenstein, M. J. Mark, and J. Zakrzewski, Recent progress on quantum simulations of non-standard Bose-Hubbard models, arXiv:2405.07775.
- V. L. Pokrovsky and A. L. Talapov, Ground state, spectrum, and phase diagram of two-dimensional incommensurate crystals, Phys. Rev. Lett. 42, 65 (1979).
- P. Bak, Commensurate phases, incommensurate phases and the devil's staircase, Rep. Prog. Phys. 45, 587 (1982).
- H. Rieger and G. Uimin, The one-dimensional ANNNI model in a transverse field: analytic and numerical study of effective Hamiltonians, Z. Phys. B 101, 597 (1996).
- P. Fendley, K. Sengupta, and S. Sachdev, Competing density-wave orders in a one-dimensional hard-boson model, Phys. Rev. B 69, 075106 (2004).
- H. Weimer and H. P. Büchler, Two-stage melting in systems of strongly interacting Rydberg atoms, Phys. Rev. Lett. 105, 230403 (2010).
- A. Bermudez, J. Almeida, K. Ott, H. Kaufmann, S. Ulm, U. Poschinger, F. Schmidt-Kaler, A. Retzker, and M. B. Plenio, Quantum magnetism of spin-ladder compounds with trapped-ion crystals, New J. Phys. 14, 093042 (2012).
- H. Weimer, String order in dipole-blockaded quantum liquids, New J. Phys. 16, 093040 (2014).
- N. Chepiga and F. Mila, Floating phase versus chiral transition in a 1D hard-boson model, Phys. Rev. Lett. 122, 017205 (2019).
- G. Giudici, A. Angelone, G. Magnifico, Z. Zeng, G. Giudice, T. Mendes-Santos, and M. Dalmonte, Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models, Phys. Rev. B 99, 094434 (2019).
- M. Rader and A. M. Läuchli, Floating phases in one-dimensional Rydberg Ising chains, arXiv:1908.02068 [cond-mat.quant-gas].
- N. Chepiga and F. Mila, Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains, Nat. Commun. 12, 414 (2021).
- I. A. Maceira, N. Chepiga, and F. Mila, Conformal and chiral phase transitions in Rydberg chains, Phys. Rev. Res. 4, 043102 (2022).
- J. Zhang, S. H. Cantú, F. Liu, A. Bylinskii, B. Braverman, F. Huber, J. Amato-Grill, A. Lukin, N. Gemelke, A. Keesling, S.-T. Wang, Y. Meurice, and S.-W. Tsai, Probing quantum floating phases in Rydberg atom arrays, Nat. Commun. 16, 712 (2025).
- J. P. Kestner, B. Wang, J. D. Sau, and S. Das Sarma, Prediction of a gapless topological Haldane liquid phase in a one-dimensional cold polar molecular lattice, Phys. Rev. B 83, 174409 (2011).
- J. Ruhman, E. G. Dalla Torre, S. D. Huber, and E. Altman, Nonlocal order in elongated dipolar gases, Phys. Rev. B 85, 125121 (2012).
- R. Thorngren, A. Vishwanath, and R. Verresen, Intrinsically gapless topological phases, Phys. Rev. B 104, 075132 (2021).
- J. Fraxanet, D. González-Cuadra, T. Pfau, M. Lewenstein, T. Langen, and L. Barbiero, Topological quantum critical points in the extended Bose-Hubbard model, Phys. Rev. Lett. 128, 043402 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/lhfx-c4xr for further details on the effective -like model explaining the floating phase, and additional results concerning models with up to next-to-NN interactions, and models with the rung hopping weaker than the leg hopping.
- J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor network Python (TeNPy), SciPost Phys. Lect. Notes 5 (2018).
- F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B 81, 064439 (2010).
- S. Ejima, F. Lange, and H. Fehske, Spectral and entanglement properties of the bosonic Haldane insulator, Phys. Rev. Lett. 113, 020401 (2014).
- P. Calabrese and A. Lefevre, Entanglement spectrum in one-dimensional systems, Phys. Rev. A 78, 032329 (2008).
- S. Gammelmark and N. T. Zinner, Dipoles on a two-leg ladder, Phys. Rev. B 88, 245135 (2013).
- D. A. Huse and M. E. Fisher, Domain walls and the melting of commensurate surface phases, Phys. Rev. Lett. 49, 793 (1982).