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Anyonic Phase Transitions in the 1D Extended Hubbard Model with Fractional Statistics

Martin Bonkhoff1,2, Kevin Jägering1, Shijie Hu1,3, Axel Pelster1, Sebastian Eggert1, and Imke Schneider1

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Phys. Rev. Lett. 135, 036601 – Published 14 July, 2025

DOI: https://doi.org/10.1103/7n1c-vq2p

Abstract

We study one-dimensional lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from bosonic to fermionic statistics by adjusting the topological exchange angle θ, which leads to a competition of different instabilities. We present the bosonization theory in the presence of dynamic gauge fields, which predicts a phase diagram of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multicritical line in the parameter space of anyonic angle θ, on-site interaction U, and nearest neighbor repulsion V. Superfluid and pair-superfluid phases are stable in a region of small V.

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References (83)

  1. J. Leinaas and J. Myrheim, On the theory of identical particles, Nuovo Cimento Soc. Ital. Fis. 37B, 1 (1977).

  2. In the original paper [1] fractional statistics for both two-dimensional and one-dimensional geometries are discussed. Our Letter refers to the 1D case.

  3. A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017).
  4. N. Goldman and J. Dalibard, Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields, Phys. Rev. X 4, 031027 (2014).
  5. M. Bukov, L. D’Alessio, and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: From dynamical stabilization to Floquet engineering, Adv. Phys. 64, 139 (2015).
  6. T. Keilmann, S. Lanzmich, I. McCulloch, and M. Roncaglia, Statistically induced phase transitions and anyons in 1D optical lattices, Nat. Commun. 2, 361 (2011).
  7. S. Greschner and L. Santos, Anyon Hubbard model in one-dimensional optical lattices, Phys. Rev. Lett. 115, 053002 (2015).
  8. F. Lange, S. Ejima, and H. Fehske, Anyonic Haldane insulator in one dimension, Phys. Rev. Lett. 118, 120401 (2017).
  9. C. Sträter, S. C. L. Srivastava, and A. Eckardt, Floquet realization and signatures of one-dimensional anyons in an optical lattice, Phys. Rev. Lett. 117, 205303 (2016).
  10. G. Tang, S. Eggert, and A. Pelster, Ground-state properties of anyons in a one-dimensional lattice, New J. Phys. 17, 123016 (2015).
  11. F. Lange, S. Ejima, and H. Fehske, Strongly repulsive anyons in one dimension, Phys. Rev. A 95, 063621 (2017).
  12. J. Arcila-Forero, R. Franco, and J. Silva-Valencia, Critical points of the anyon-Hubbard model, Phys. Rev. A 94, 013611 (2016).
  13. J. Arcila-Forero, R. Franco, and J. Silva-Valencia, Three-body-interaction effects on the ground state of one-dimensional anyons, Phys. Rev. A 97, 023631 (2018).
  14. M. Bonkhoff, S. B. Jäger, I. Schneider, A. Pelster, and S. Eggert, Coherence properties of the repulsive anyon-Hubbard dimer, Phys. Rev. B 108, 155134 (2023).
  15. F. Görg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, and T. Esslinger, Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter, Nat. Phys. 15, 1161 (2019).
  16. 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).
  17. J. Kwan, P. Segura, Y. Li, S. Kim, A. V. Gorshkov, A. Eckardt, B. Bakkali-Hassani, and M. Greiner, Realization of one-dimensional anyons with arbitrary statistical phase, Science 386, 1055 (2024).
  18. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  19. 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).
  20. 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).
  21. 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).
  22. S. Fazzini, P. Chudzinski, C. Dauer, I. Schneider, and S. Eggert, Nonequilibrium Floquet steady states of time-periodic driven Luttinger liquids, Phys. Rev. Lett. 126, 243401 (2021).
  23. C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices, Nat. Phys. 15, 1168 (2019).
  24. T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold atoms out of equilibrium, Annu. Rev. Condens. Matter Phys. 6, 201 (2015).
  25. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  26. 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).
  27. C. S. Chisholm, A. Frölian, E. Neri, R. Ramos, L. Tarruell, and A. Celi, Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate, Phys. Rev. Res. 4, 043088 (2022).
  28. S. Dhar, B. Wang, M. Horvath, A. Vashisht, Y. Zeng, M. B. Zvonarev, N. Goldman, Y. Guo, M. Landini, and H.-C. Nägerl, Observing anyonization of bosons in a quantum gas, Nature (London) 642, 53 (2025).
  29. M. Bonkhoff, K. Jägering, S. Eggert, A. Pelster, M. Thorwart, and T. Posske, Bosonic continuum theory of one-dimensional lattice anyons, Phys. Rev. Lett. 126, 163201 (2021).
  30. M. Nakamura, Mechanism of CDW-SDW transition in one dimension, J. Phys. Soc. Jpn. 68, 3123 (1999).
  31. P. Sengupta, A. W. Sandvik, and D. K. Campbell, Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model, Phys. Rev. B 65, 155113 (2002).
  32. A. W. Sandvik, L. Balents, and D. K. Campbell, Ground state phases of the half-filled one-dimensional extended Hubbard model, Phys. Rev. Lett. 92, 236401 (2004).
  33. L. Barbiero, S. Fazzini, and A. Montorsi, Non-local order parameters as a probe for phase transitions in the extended Fermi-Hubbard model, Eur. Phys. J. Spec. Top. 226, 2697 (2017).
  34. E. G. Dalla Torre, E. Berg, and E. Altman, Hidden order in 1D Bose insulators, Phys. Rev. Lett. 97, 260401 (2006).
  35. E. Berg, E. G. Dalla Torre, T. Giamarchi, and E. Altman, Rise and fall of hidden string order of lattice Bosons, Phys. Rev. B 77, 245119 (2008).
  36. S. Ejima, F. Lange, and H. Fehske, Spectral and entanglement properties of the Bosonic Haldane insulator, Phys. Rev. Lett. 113, 020401 (2014).
  37. D. Rossini and R. Fazio, Phase diagram of the extended Bose Hubbard model, New J. Phys. 14, 065012 (2012).
  38. M. Dalmonte, M. Di Dio, L. Barbiero, and F. Ortolani, Homogeneous and inhomogeneous magnetic phases of constrained dipolar Bosons, Phys. Rev. B 83, 155110 (2011).
  39. H. J. Schulz, Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number, Phys. Rev. B 34, 6372 (1986).
  40. See Supplemental Material at http://link.aps.org/supplemental/10.1103/7n1c-vq2p for details about the lattice gauge function, bosonization, symmetry transformations, and behavior of the order parameter.
  41. T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2003).
  42. P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory, Graduate Texts in Contemporary Physics (Springer, New York, 1997).
  43. G. I. Japaridze and A. P. Kampf, Weak-coupling phase diagram of the extended Hubbard model with correlated-hopping interaction, Phys. Rev. B 59, 12822 (1999).
  44. P. Lecheminant, A. O. Gogolin, and A. A. Nersesyan, Criticality in self-dual sine-Gordon models, Nucl. Phys. B639, 502 (2002).
  45. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  46. S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
  47. I. P. McCulloch, Infinite size density matrix renormalization group, revisited, arXiv:0804.2509.
  48. T. Ogino, S. Furukawa, R. Kaneko, S. Morita, and N. Kawashima, Symmetry-protected topological phases and competing orders in a spin-12 XXZ ladder with a four-spin interaction, Phys. Rev. B 104, 075135 (2021).
  49. S. Nishimoto, Tomonaga-Luttinger-liquid criticality: Numerical entanglement entropy approach, Phys. Rev. B 84, 195108 (2011).
  50. R. A. Macêdo, F. B. Ramos, and R. G. Pereira, Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions, Phys. Rev. B 105, 205144 (2022).
  51. C. Mudry, A. Furusaki, T. Morimoto, and T. Hikihara, Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited, Phys. Rev. B 99, 205153 (2019).
  52. 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).
  53. R.-Z. Huang, D.-C. Lu, Y.-Z. You, Z. Y. Meng, and T. Xiang, Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point, Phys. Rev. B 100, 125137 (2019).
  54. B. Roberts, S. Jiang, and O. I. Motrunich, Deconfined quantum critical point in one dimension, Phys. Rev. B 99, 165143 (2019).
  55. Q. Luo, S. Hu, J. Li, J. Zhao, H.-Y. Kee, and X. Wang, Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy, Phys. Rev. B 107, 245131 (2023).
  56. C. Zhang and M. Levin, Exactly solvable model for a deconfined quantum critical point in 1D, Phys. Rev. Lett. 130, 026801 (2023).
  57. T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm, Phys. Rev. B 70, 144407 (2004).
  58. M. Levin and T. Senthil, Deconfined quantum criticality and Néel order via dimer disorder, Phys. Rev. B 70, 220403(R) (2004).
  59. C. Wang, A. Nahum, M. A. Metlitski, C. Xu, and T. Senthil, Deconfined quantum critical points: Symmetries and dualities, Phys. Rev. X 7, 031051 (2017).
  60. L. Landau and E. Lifshitz, Statistical Physics, Part I, Vol. 5 (Elsevier Butterworth-Heinemann, Oxford, 1980).
  61. J. D’Emidio, A. A. Eberharter, and A. M. Läuchli, Diagnosing weakly first-order phase transitions by coupling to order parameters, SciPost Phys. 15, 061 (2023).
  62. M. Song, J. Zhao, M. Cheng, C. Xu, M. M. Scherer, L. Janssen, and Z. Y. Meng, Evolution of entanglement entropy at SU(n) deconfined quantum critical points, Sci. Adv. 11, eadr0634 (2025).
  63. S. Ejima and H. Fehske, Comparative density-matrix renormalization group study of symmetry-protected topological phases in spin-1 chain and Bose-Hubbard models, Phys. Rev. B 91, 045121 (2015).
  64. 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).
  65. S. Eggert, Numerical evidence for multiplicative logarithmic corrections from marginal operators, Phys. Rev. B 54, R9612 (1996).
  66. S. Miyakoshi, S. Nishimoto, and Y. Ohta, Entanglement properties of the Haldane phases: A finite system-size approach, Phys. Rev. B 94, 235155 (2016).
  67. L. Wang and A. W. Sandvik, Critical level crossings and gapless spin liquid in the square-lattice spin-1/2 J1−J2 Heisenberg antiferromagnet, Phys. Rev. Lett. 121, 107202 (2018).
  68. T. Wang, S. Hu, S. Eggert, M. Fleischhauer, A. Pelster, and X.-F. Zhang, Floquet-induced superfluidity with periodically modulated interactions of two-species hardcore bosons in a one-dimensional optical lattice, Phys. Rev. Res. 2, 013275 (2020).
  69. P. Zhong, T. Wang, S. Hu, and H. Lin, Quantum phase diagram for two-species hardcore bosons in one-dimensional optical lattices with resonantly driven Rabi frequency, Phys. Rev. B 106, 045130 (2022).
  70. J.-L. He, S. Eggert, H. Lin, X. Wang, and S. J. Hu, Competition between dimerization and vector chirality in the spin-3/2 J2−J2 Heisenberg chain with uniaxial single-ion anisotropy, Phys. Rev. B 110, 195129 (2024).
  71. W.-L. You, Y.-W. Li, and S.-J. Gu, Fidelity, dynamic structure factor, and susceptibility in critical phenomena, Phys. Rev. E 76, 022101 (2007).
  72. P. Zanardi and N. Paunković, Ground state overlap and quantum phase transitions, Phys. Rev. E 74, 031123 (2006).
  73. X. Wang, Boundary and impurity effects on the entanglement of Heisenberg chains, Phys. Rev. E 69, 066118 (2004).
  74. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Scaling of entanglement close to a quantum phase transition, Nature (London) 416, 608 (2002).
  75. Q. Luo, S. Hu, B. Xi, J. Zhao, and X. Wang, Ground-state phase diagram of an anisotropic spin-12 model on the triangular lattice, Phys. Rev. B 95, 165110 (2017).
  76. Q. Luo, S. Hu, J. Zhao, A. Metavitsiadis, S. Eggert, and X. Wang, Ground-state phase diagram of the frustrated spin-12 two-leg honeycomb ladder, Phys. Rev. B 97, 214433 (2018).
  77. T. Sowiński, R. W. Chhajlany, O. Dutta, L. Tagliacozzo, and M. Lewenstein, Criticality in the Bose-Hubbard model with three-body repulsion, Phys. Rev. A 92, 043615 (2015).
  78. N. Cuzzuol, L. Barbiero, and A. Montorsi, Nonlocal order parameter of pair superfluids, SciPost Phys. Core 8, 020 (2025).
  79. A. J. Daley, J. M. Taylor, S. Diehl, M. Baranov, and P. Zoller, Atomic three-body loss as a dynamical three-body interaction, Phys. Rev. Lett. 102, 040402 (2009).
  80. Y.-W. Lee and M.-F. Yang, Superfluid-insulator transitions in attractive Bose-Hubbard model with three-body constraint, Phys. Rev. A 81, 061604(R) (2010).
  81. Y.-C. Chen, K.-K. Ng, and M.-F. Yang, Quantum phase transitions in the attractive extended Bose-Hubbard model with a three-body constraint, Phys. Rev. B 84, 092503 (2011).
  82. L. Bonnes and S. Wessel, Pair superfluidity of three-body constrained Bosons in two dimensions, Phys. Rev. Lett. 106, 185302 (2011).
  83. K.-K. Ng and M.-F. Yang, Thermal phase transitions in the attractive extended Bose-Hubbard model with three-body constraint, Phys. Rev. B 83, 100511(R) (2011).

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Phys. Rev. Lett. 135, 036601– Published 14 July, 2025
  • Received 30 July 2024
  • Revised 13 April 2025
  • Accepted 16 June 2025
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