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Boson-Gutzwiller quantum liquids on a lattice

Daniel Pérez-Cruz1 and Manuel Valiente2

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Phys. Rev. Research 7, 023310 – Published 26 June, 2025

DOI: https://doi.org/10.1103/lvqx-g5l2

Abstract

We consider one-dimensional, interacting spinless bosons on a tight-binding lattice described by the Bose-Hubbard model. Besides attractive onsite two-body interactions, we include a three-body repulsive term such that the competition between these two forces allows the formation of self-bound liquid states. We investigate the properties of this system using the Gutzwiller approximation, showing that, indeed, this mean-field approach also supports liquid states. We find that for densities lower than the equilibrium density, the Gutzwiller method and other mean-field approaches—such as the Gross-Pitaevskii theory—feature a sharp transition to the vacuum state. This, however, is avoided by considering local minima of the functional in the standard manner. We also study the excitation spectrum, and calculate the speed of sound, in full agreement with the usual expression obtained from the thermodynamic equation of state. We study their corresponding quantum droplets variationally and find that the results behave in accordance with the one-dimensional liquid-drop model.

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References (44)

  1. D. Pines and P. Nozières, The Theory of Quantum Liquids: Normal Fermi liquids, Advanced Book Classics (CRC Press, Boca Raton, 1989).
  2. C. Cabrera, L. Tanzi, J. Sanz, B. Naylor, P. Thomas, P. Cheiney, and L. Tarruell, Quantum liquid droplets in a mixture of Bose-Einstein condensates, Science 359, 301 (2018).
  3. M. Schmitt, M. Wenzel, F. Böttcher, I. Ferrier-Barbut, and T. Pfau, Self-bound droplets of a dilute magnetic quantum liquid, Nature (London) 539, 259 (2016).
  4. I. Ferrier-Barbut, H. Kadau, M. Schmitt, M. Wenzel, and T. Pfau, Observation of quantum droplets in a strongly dipolar Bose gas, Phys. Rev. Lett. 116, 215301 (2016).
  5. G. Ferioli, G. Semeghini, L. Masi, G. Giusti, G. Modugno, M. Inguscio, A. Gallemí, A. Recati, and M. Fattori, Collisions of self-bound quantum droplets, Phys. Rev. Lett. 122, 090401 (2019).
  6. F. Böttcher, J.-N. Schmidt, M. Wenzel, J. Hertkorn, M. Guo, T. Langen, and T. Pfau, Transient supersolid properties in an array of dipolar quantum droplets, Phys. Rev. X 9, 011051 (2019).
  7. G. Semeghini, G. Ferioli, L. Masi, C. Mazzinghi, L. Wolswijk, F. Minardi, M. Modugno, G. Modugno, M. Inguscio, and M. Fattori, Self-bound quantum droplets of atomic mixtures in free space, Phys. Rev. Lett. 120, 235301 (2018).
  8. D. Petrov, Quantum mechanical stabilization of a collapsing Bose-Bose mixture, Phys. Rev. Lett. 115, 155302 (2015).
  9. D. Petrov and G. Astrakharchik, Ultradilute low-dimensional liquids, Phys. Rev. Lett. 117, 100401 (2016).
  10. I. Morera, G. E. Astrakharchik, A. Polls, and B. Juliá-Díaz, Quantum droplets of bosonic mixtures in a one-dimensional optical lattice, Phys. Rev. Res. 2, 022008 (2020).
  11. I. Morera, B. Juliá-Díaz, and M. Valiente, Universality of quantum liquids and droplets in one dimension, Phys. Rev. Res. 4, L042024 (2022).
  12. M. Valiente, Three-body repulsive forces among identical bosons in one dimension, Phys. Rev. A 100, 013614 (2019).
  13. H.-W. Hammer, A. Nogga, and A. Schwenk, Colloquium: Three-body forces: From cold atoms to nuclei, Rev. Mod. Phys. 85, 197 (2013).
  14. T. Sowiński and R. W. Chhajlany, Mean-field approaches to the Bose–Hubbard model with three-body local interaction, Phys. Scr. 2014, 014038 (2014).
  15. A. Pricoupenko and D. Petrov, Three-body interaction near a narrow two-body zero crossing, Phys. Rev. A 100, 042707 (2019).
  16. D.-S. Lühmann, Cluster Gutzwiller method for bosonic lattice systems, Phys. Rev. A 87, 043619 (2013).
  17. I. Carusotto and Y. Castin, An exact reformulation of the Bose–Hubbard model in terms of a stochastic Gutzwiller ansatz, New J. Phys. 5, 91 (2003).
  18. P. Buonsante, F. Massel, V. Penna, and A. Vezzani, Gutzwiller approach to the Bose-Hubbard model with random local impurities, Phys. Rev. A 79, 013623 (2009).
  19. M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B 40, 546 (1989).
  20. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold bosonic atoms in optical lattices, Phys. Rev. Lett. 81, 3108 (1998).
  21. M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, One dimensional bosons: From condensed matter systems to ultracold gases, Rev. Mod. Phys. 83, 1405 (2011).
  22. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  23. D. S. Rokhsar and B. Kotliar, Gutzwiller projection for bosons, Phys. Rev. B 44, 10328 (1991).
  24. M. C. Gutzwiller, Effect of correlation on the ferromagnetism of transition metals, Phys. Rev. Lett. 10, 159 (1963).
  25. W. Krauth, M. Caffarel, and J.-P. Bouchaud, Gutzwiller wave function for a model of strongly interacting bosons, Phys. Rev. B 45, 3137 (1992).
  26. K. Sheshadri, H. Krishnamurthy, R. Pandit, and T. Ramakrishnan, Superfluid and insulating phases in an interacting-boson model: Mean-field theory and the RPA, Europhys. Lett. 22, 257 (1993).
  27. F. Caleffi, M. Capone, C. Menotti, I. Carusotto, and A. Recati, Quantum fluctuations beyond the Gutzwiller approximation in the Bose-Hubbard model, Phys. Rev. Res. 2, 033276 (2020).
  28. T. Jolicoeur and J. C. Le Guillou, Fluctuations beyond the Gutzwiller approximation in the slave-boson approach, Phys. Rev. B 44, 2403 (1991).
  29. G. Astrakharchik and B. A. Malomed, Dynamics of one-dimensional quantum droplets, Phys. Rev. A 98, 013631 (2018).
  30. K. V. Krutitsky and P. Navez, Excitation dynamics in a lattice Bose gas within the time-dependent Gutzwiller mean-field approach, Phys. Rev. A 84, 033602 (2011).
  31. J. Zakrzewski, Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms, Phys. Rev. A 71, 043601 (2005).
  32. C. Trefzger, C. Menotti, and M. Lewenstein, Ultracold dipolar gas in an optical lattice: The fate of metastable states, Phys. Rev. A 78, 043604 (2008).
  33. S. D. Huber, B. Theiler, E. Altman, and G. Blatter, Amplitude mode in the quantum phase model, Phys. Rev. Lett. 100, 050404 (2008).
  34. Z.-H. Luo, W. Pang, B. Liu, Y.-Y. Li, and B. A. Malomed, A new form of liquid matter: Quantum droplets, Front. Phys. 16, 32201 (2021).
  35. F. Dalfovo, A. Lastri, L. Pricaupenko, S. Stringari, and J. Treiner, Structural and dynamical properties of superfluid helium: a density-functional approach, Phys. Rev. B 52, 1193 (1995).
  36. For the droplets, since their average size is much larger than the lattice spacing, we have indistinctly used the usual continuous derivative. Since J=1/2m the kinetic term reads T[ρ]=J|dρdx|2.
  37. D. Sprung and J. Martorell, The symmetrized Fermi function and its transforms, J. Phys. A: Math. Gen. 30, 6525 (1997).
  38. S. A. Chin and E. Krotscheck, Structure and collective excitations of He4 clusters, Phys. Rev. B 45, 852 (1992).
  39. V. Pandharipande, S. C. Pieper, and R. Wiringa, Variational Monte Carlo calculations of ground states of liquid He4 and He3 drops, Phys. Rev. B 34, 4571 (1986).
  40. S. Stringari and J. Treiner, Systematics of liquid helium clusters, J. Chem. Phys. 87, 5021 (1987).
  41. T. G. Skov, M. G. Skou, N. B. Jørgensen, and J. J. Arlt, Observation of a Lee-Huang-Yang fluid, Phys. Rev. Lett. 126, 230404 (2021).
  42. Z. Guo, F. Jia, L. Li, Y. Ma, J. M. Hutson, X. Cui, and D. Wang, Lee-Huang-Yang effects in the ultracold mixture of Na23 and Rb87 with attractive interspecies interactions, Phys. Rev. Res. 3, 033247 (2021).
  43. T. D. Lee, K. Huang, and C. N. Yang, Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties, Phys. Rev. 106, 1135 (1957).
  44. J. Treiner, W. Myers, W. Swiatecki, and M. Weiss, Bulk compression due to surface tension in Hartree-Fock, Thomas-Fermi and Droplet-model calculations, Nucl. Phys. A 452, 93 (1986).

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Phys. Rev. Research 7, 023310– Published 26 June, 2025
  • Received 25 February 2025
  • Accepted 11 June 2025
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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.

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