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Emergent chiral Higgs mode in π-flux frustrated lattices

M. Lanaro1,2, L. Maffi1,2, and M. Di Liberto1,2,3,*

  • *Contact author: marco.diliberto@unipd.it
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Phys. Rev. B 114, 225126 – Published 15 October, 2026

DOI: https://doi.org/10.1103/tfbh-ncfw

Abstract

Neutral-atom quantum simulators provide a powerful platform for realizing strongly correlated phases, enabling access to dynamical signatures of quasiparticles and symmetry breaking processes. Motivated by recent observations of quantum phases in flux-frustrated ladders with nonvanishing ground-state currents, we investigate interacting bosons on the dimerized Benalcazar-Bernevig-Hughes (BBH) lattice in two dimensions—originally introduced in the context of higher-order topology. After mapping out the phase diagram, which includes vortex superfluid (V-SF), vortex Mott insulator (V-MI), and featureless Mott insulator (MI) phases, we focus on the integer filling case. There, the MI/V-SF transition breaks the Z2T and U(1) symmetries, where Z2T corresponds to time-reversal symmetry (TRS). Using a slave boson description, we resolve the excitation spectrum across the transition and uncover a chiral Higgs mode whose mass softens at criticality, providing a dynamical hallmark of emergent chirality that manifests via the oscillation of the loop currents in quench dynamics. Our results establish an experimentally realistic setting for probing unconventional TRS-broken phases and quasiparticles with intrinsic chirality in strongly interacting quantum matter.

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References (114)

  1. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  2. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  3. T. Fukuhara, P. Schauß, M. Endres, S. Hild, M. Cheneau, I. Bloch, and C. Gross, Microscopic observation of magnon bound states and their dynamics, Nature (London) 502, 76 (2013).
  4. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  5. J. Koepsell, J. Vijayan, P. Sompet, F. Grusdt, T. A. Hilker, E. Demler, G. Salomon, I. Bloch, and C. Gross, Imaging magnetic polarons in the doped Fermi–Hubbard model, Nature (London) 572, 358 (2019).
  6. M. L. Prichard, Z. Ba, I. Morera, B. M. Spar, D. A. Huse, E. Demler, and W. S. Bakr, Magnon-polarons in the Fermi–Hubbard model, Nat. Phys. 21, 1548 (2025).
  7. C. Chen, G. Emperauger, G. Bornet, F. Caleca, B. Gély, M. Bintz, S. Chatterjee, V. Liu, D. Barredo, N. Y. Yao, T. Lahaye, F. Mezzacapo, T. Roscilde, and A. Browaeys, Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator, Science 389, 483 (2025).
  8. D. Pekker and C. M. Varma, Amplitude/Higgs modes in condensed matter physics, Annu. Rev. Condens. Matter Phys. 6, 269 (2015).
  9. U. Bissbort, S. Götze, Y. Li, J. Heinze, J. S. Krauser, M. Weinberg, C. Becker, K. Sengstock, and W. Hofstetter, Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering, Phys. Rev. Lett. 106, 205303 (2011).
  10. M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauβ, C. Gross, E. Demler, S. Kuhr, and I. Bloch, The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature (London) 487, 454 (2012).
  11. A. Behrle, T. Harrison, J. Kombe, K. Gao, M. Link, J.-S. Bernier, C. Kollath, and M. Köhl, Higgs mode in a strongly interacting fermionic superfluid, Nat. Phys. 14, 781 (2018).
  12. A. Kell, M. Breyer, D. Eberz, and M. Köhl, Exciting the Higgs mode in a strongly interacting Fermi gas by interaction modulation, Phys. Rev. Lett. 133, 150403 (2024).
  13. J. Léonard, A. Morales, P. Zupancic, T. Donner, and T. Esslinger, Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas, Science 358, 1415 (2017).
  14. T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Koyluoglu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kalinowski, S. Sachdev, D. A. Huse, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum coarsening and collective dynamics on a programmable simulator, Nature (London) 638, 86 (2025).
  15. J. Hertkorn, F. Böttcher, M. Guo, J. N. Schmidt, T. Langen, H. P. Büchler, and T. Pfau, Fate of the amplitude mode in a trapped dipolar supersolid, Phys. Rev. Lett. 123, 193002 (2019).
  16. M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra, P. R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliūnas, V. Kasper, A. Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T. V. Zache, J. Zakrzewski, et al., Cold atoms meet lattice gauge theory, Philos. Trans. R. Soc. A 380, 20210064 (2022).
  17. J. C. Halimeh, M. Aidelsburger, F. Grusdt, P. Hauke, and B. Yang, Cold-atom quantum simulators of gauge theories, Nat. Phys. 21, 25 (2025).
  18. D. Jaksch and P. Zoller, Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms, New J. Phys. 5, 56 (2003).
  19. 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).
  20. N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys. 12, 639 (2016).
  21. N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
  22. R. B. Laughlin, Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50, 1395 (1983).
  23. R. E. Prange and S. M. Girvin, The Quantum Hall effect (Springer, Berlin, 1987).
  24. B. I. Halperin, Statistics of quasiparticles and the hierarchy of fractional quantized Hall states, Phys. Rev. Lett. 52, 1583 (1984).
  25. A. Stern, Anyons and the quantum Hall effect—A pedagogical review, Ann. Phys. 323, 204 (2008).
  26. F. D. M. Haldane, Geometrical description of the fractional quantum Hall effect, Phys. Rev. Lett. 107, 116801 (2011).
  27. J. Liang, Z. Liu, Z. Yang, Y. Huang, U. Wurstbauer, C. R. Dean, K. W. West, L. N. Pfeiffer, L. Du, and A. Pinczuk, Evidence for chiral graviton modes in fractional quantum Hall liquids, Nature (London) 628, 78 (2024).
  28. Z. Bacciconi, H. B. Xavier, I. Carusotto, T. Chanda, and M. Dalmonte, Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons, Phys. Rev. X 15, 021027 (2025).
  29. H. B. Xavier, Z. Bacciconi, T. Chanda, D. T. Son, and M. Dalmonte, Chiral graviton modes on the lattice, Phys. Rev. Lett. 135, 196501 (2025).
  30. J. Léonard, S. Kim, J. Kwan, P. Segura, F. Grusdt, C. Repellin, N. Goldman, and M. Greiner, Realization of a fractional quantum Hall state with ultracold atoms, Nature (London) 619, 495 (2023).
  31. P. Lunt, P. Hill, J. Reiter, P. M. Preiss, M. Gałka, and S. Jochim, Realization of a Laughlin state of two rapidly rotating fermions, Phys. Rev. Lett. 133, 253401 (2024).
  32. J. Kwan, P. Segura, Y. Li, T. Blatz, A. Zhi, B. Bakkali-Hassani, A. Bohrdt, M. Greiter, F. Grusdt, and M. Greiner, A Pfaffian quantum Hall state of ultracold bosons, arXiv:2606.12409.
  33. S. J. Evered, M. Kalinowski, A. A. Geim, T. Manovitz, D. Bluvstein, S. H. Li, N. Maskara, H. Zhou, S. Ebadi, M. Xu, J. Campo, M. Cain, S. Ostermann, S. F. Yelin, S. Sachdev, M. Greiner, V. Vuletić, and M. D. Lukin, Probing the Kitaev honeycomb model on a neutral-atom quantum computer, Nature (London) 645, 341 (2025).
  34. 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).
  35. S. Greschner, M. Filippone, and T. Giamarchi, Universal Hall response in interacting quantum systems, Phys. Rev. Lett. 122, 083402 (2019).
  36. 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).
  37. A. Impertro, S. J. Huh, S. Karch, J. F. Wienand, I. Bloch, and M. Aidelsburger, Strongly interacting Meissner phases in large bosonic flux ladders, Nat. Phys. 21, 895 (2025).
  38. E. Orignac and T. Giamarchi, Meissner effect in a bosonic ladder, Phys. Rev. B 64, 144515 (2001).
  39. C. L. Kane, R. Mukhopadhyay, and T. C. Lubensky, Fractional quantum Hall effect in an array of quantum wires, Phys. Rev. Lett. 88, 036401 (2002).
  40. M. Calvanese Strinati, E. Cornfeld, D. Rossini, S. Barbarino, M. Dalmonte, R. Fazio, E. Sela, and L. Mazza, Laughlin-like states in bosonic and fermionic atomic synthetic ladders, Phys. Rev. X 7, 021033 (2017).
  41. M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, Realization of fully frustrated Josephson-junction arrays with cold atoms, Phys. Rev. Lett. 95, 010401 (2005).
  42. L.-K. Lim, C. M. Smith, and A. Hemmerich, Staggered-vortex superfluid of ultracold bosons in an optical lattice, Phys. Rev. Lett. 100, 130402 (2008).
  43. M.-C. Cha and J.-G. Shin, Two peaks in the momentum distribution of bosons in a weakly frustrated two-leg optical ladder, Phys. Rev. A 83, 055602 (2011).
  44. A. Dhar, T. Mishra, M. Maji, R. V. Pai, S. Mukerjee, and A. Paramekanti, Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model, Phys. Rev. B 87, 174501 (2013).
  45. S. Greschner, L. Santos, and T. Vekua, Ultracold bosons in zig-zag optical lattices, Phys. Rev. A 87, 033609 (2013).
  46. 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).
  47. F. Kolley, M. Piraud, I. P. McCulloch, U. Schollwöck, and F. Heidrich-Meisner, Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux, New J. Phys. 17, 092001 (2015).
  48. 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(R) (2015).
  49. 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).
  50. A. Petrescu, M. Piraud, G. Roux, I. P. McCulloch, and K. Le Hur, Precursor of the Laughlin state of hard-core bosons on a two-leg ladder, Phys. Rev. B 96, 014524 (2017).
  51. 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).
  52. C.-M. Halati and T. Giamarchi, Bose-Hubbard triangular ladder in an artificial gauge field, Phys. Rev. Res. 5, 013126 (2023).
  53. M. Di Liberto and N. Goldman, Chiral orbital order of interacting bosons without higher bands, Phys. Rev. Res. 5, 023064 (2023).
  54. L. Barbiero, J. Cabedo, M. Lewenstein, L. Tarruell, and A. Celi, Frustrated magnets without geometrical frustration in bosonic flux ladders, Phys. Rev. Res. 5, L042008 (2023).
  55. A. Dasgupta, M. Łącki, H. Korbmacher, G. A. Domínguez-Castro, J. Zakrzewski, and L. Santos, Chiral phases and dynamics of dipoles in triangular optical ladders, Phys. Rev. A 113, L031301 (2026).
  56. M. Hasan, L. Donini, S. Shanokprasith, D. Braund, T. Marozsak, M. Epping, D. Reed, M. Melchner, T. Harte, and U. Schneider, Superfluid-Mott transition in a frustrated triangular optical lattice, arXiv:2509.20352.
  57. R. Citro, T. Giamarchi, and E. Orignac, Hall response in interacting bosonic and fermionic ladders, Phys. Rev. Lett. 134, 056501 (2025).
  58. A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall states of atoms in optical lattices, Phys. Rev. Lett. 94, 086803 (2005).
  59. M. Hafezi, A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall effect in optical lattices, Phys. Rev. A 76, 023613 (2007).
  60. Y.-C. He, S. Bhattacharjee, R. Moessner, and F. Pollmann, Bosonic integer quantum Hall effect in an interacting lattice model, Phys. Rev. Lett. 115, 116803 (2015).
  61. J. Boesl, R. Dilip, F. Pollmann, and M. Knap, Characterizing fractional topological phases of lattice bosons near the first Mott lobe, Phys. Rev. B 105, 075135 (2022).
  62. H. Kamal, J. Kemp, Y.-C. He, Y. Fuji, M. Aidelsburger, P. Zoller, and N. Y. Yao, Floquet flux attachment in cold atomic systems, Phys. Rev. Lett. 133, 163403 (2024).
  63. X.-G. Wen, Colloquium: Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89, 041004 (2017).
  64. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Quantized electric multipole insulators, Science 357, 61 (2017).
  65. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators, Phys. Rev. B 96, 245115 (2017).
  66. X. Li, E. Zhao, and W. V. Liu, Effective action approach to the p-band Mott insulator and superfluid transition, Phys. Rev. A 83, 063626 (2011).
  67. P. Soltan-Panahi, D.-S. Lühmann, J. Struck, P. Windpassinger, and K. Sengstock, Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices, Nat. Phys. 8, 71 (2012).
  68. O. Jürgensen, K. Sengstock, and D.-S. Lühmann, Twisted complex superfluids in optical lattices, Sci. Rep. 5, 12912 (2015).
  69. D.-S. Lühmann, Cluster Gutzwiller method for bosonic lattice systems, Phys. Rev. A 87, 043619 (2013).
  70. D. Yamamoto, A. Masaki, and I. Danshita, Quantum phases of hardcore bosons with long-range interactions on a square lattice, Phys. Rev. B 86, 054516 (2012).
  71. D. Huerga, J. Dukelsky, and G. E. Scuseria, Composite boson mapping for lattice boson systems, Phys. Rev. Lett. 111, 045701 (2013).
  72. D. Yamamoto, G. Marmorini, and I. Danshita, Quantum phase diagram of the triangular-lattice XXZ model in a magnetic field, Phys. Rev. Lett. 112, 127203 (2014).
  73. G. C. Paul, P. Recher, and L. Santos, Interacting Bose gases in twisted-bilayer optical lattices, Phys. Rev. A 113, 013324 (2026).
  74. W. Krauth, M. Caffarel, and J.-P. Bouchaud, Gutzwiller wave function for a model of strongly interacting bosons, Phys. Rev. B 45, 3137 (1992).
  75. 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).
  76.  A single-site ansatz is described by a wave function |ψi〉=∑ncn|n〉. Using such an ansatz, the fractional filling condition, e.g., 〈n̂i〉=1/2, necessarily implies 〈b̂i〉≠0. This forbids the possibility to capture phase transitions into insulating phases with fractional filling within a single-site Gutzwiller ansatz.
  77. See Supplemental Material at http://link.aps.org/supplemental/10.1103/tfbh-ncfw for details on the slave boson calculations, additional excitation spectra, and DMRG results with the tree tensor network ansatz, which includes Refs. [109, 110, 111, 112, 113, 114].
  78. A. Isacsson and S. M. Girvin, Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice, Phys. Rev. A 72, 053604 (2005).
  79. W. V. Liu and C. Wu, Atomic matter of nonzero-momentum Bose-Einstein condensation and orbital current order, Phys. Rev. A 74, 013607 (2006).
  80. G. Wirth, M. Ölschläger, and A. Hemmerich, Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice, Nat. Phys. 7, 147 (2011).
  81. X. Li and W. V. Liu, Physics of higher orbital bands in optical lattices: A review, Rep. Prog. Phys. 79, 116401 (2016).
  82. X. Li, Z. Zhang, and W. V. Liu, Time-reversal symmetry breaking of p-orbital bosons in a one-dimensional optical lattice, Phys. Rev. Lett. 108, 175302 (2012).
  83. E. Loh Jr., D. J. Scalapino, and P. M. Grant, Monte Carlo simulations of the quantum XXZ model in two dimensions, Phys. Scr. 32, 327 (1985).
  84. A. Cuccoli, T. Roscilde, V. Tognetti, R. Vaia, and P. Verrucchi, Phase transitions in two-dimensional anisotropic quantum magnets, Eur. Phys. J. B 20, 55 (2001).
  85. D. Peter, S. Müller, S. Wessel, and H. P. Büchler, Anomalous behavior of spin systems with dipolar interactions, Phys. Rev. Lett. 109, 025303 (2012).
  86. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases, 4 (2022).
  87. J. Carrasquilla, S. R. Manmana, and M. Rigol, Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model, Phys. Rev. A 87, 043606 (2013).
  88.  A similar behavior is identified also in a small 2D system via tree tensor network calculation, as shown in Ref. [77].
  89. S. Sachdev, Quantum Phases of Matter (Cambridge University Press, Cambridge, 2023).
  90. E. Altman and A. Auerbach, Oscillating superfluidity of bosons in optical lattices, Phys. Rev. Lett. 89, 250404 (2002).
  91. I. Frérot and T. Roscilde, Entanglement entropy across the superfluid-insulator transition: A signature of bosonic criticality, Phys. Rev. Lett. 116, 190401 (2016).
  92. D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, Ultracold atoms in optical lattices, Phys. Rev. A 68, 043623 (2003).
  93. S. D. Huber, E. Altman, H. P. Büchler, and G. Blatter, Dynamical properties of ultracold bosons in an optical lattice, Phys. Rev. B 75, 085106 (2007).
  94. K. V. Krutitsky, Ultracold bosons with short-range interaction in regular optical lattices, Phys. Rep. 607, 1 (2016).
  95. M. Di Liberto, A. Recati, N. Trivedi, I. Carusotto, and C. Menotti, Particle-hole character of the Higgs and Goldstone modes in strongly interacting lattice bosons, Phys. Rev. Lett. 120, 073201 (2018).
  96. J. Wang, Y. Deng, and W. Zheng, Topological Higgs amplitude modes in strongly interacting superfluids, Phys. Rev. A 104, 043328 (2021).
  97. 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).
  98. D. Podolsky, A. Auerbach, and D. P. Arovas, Visibility of the amplitude (Higgs) mode in condensed matter, Phys. Rev. B 84, 174522 (2011).
  99. A. Impertro, S. Karch, J. F. Wienand, S. J. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Local readout and control of current and kinetic energy operators in optical lattices, Phys. Rev. Lett. 133, 063401 (2024).
  100. L. Pollet and N. Prokof'ev, Higgs mode in a two-dimensional superfluid, Phys. Rev. Lett. 109, 010401 (2012).
  101. J. Bibo, I. Lovas, Y. You, F. Grusdt, and F. Pollmann, Fractional corner charges in a two-dimensional superlattice Bose-Hubbard model, Phys. Rev. B 102, 041126(R) (2020).
  102. D. González-Cuadra, Higher-order topological quantum paramagnets, Phys. Rev. B 105, L020403 (2022).
  103. F. Grusdt, M. Höning, and M. Fleischhauer, Topological edge states in the one-dimensional superlattice Bose-Hubbard model, Phys. Rev. Lett. 110, 260405 (2013).
  104. M. Burgher, M. Di Liberto, N. Goldman, and I. Amelio, Fate of chiral order and impurity self-pinning in flat bands with local symmetry, Phys. Rev. B 111, 064514 (2025).
  105. A. A. Stepanenko and M. Di Liberto, Vortex bound states in dimerized π-flux optical lattices: Characterization, state preparation, and current measurement, Phys. Rev. A 110, L061304 (2024).
  106. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Deconfined quantum critical points, Science 303, 1490 (2004).
  107. T. Senthil, Deconfined quantum critical points: A review, in 50 Years of the Renormalization Group Dedicated to the Memory of Michael E. Fisher, edited by A. Aharony, O. Entin-Wohlman, D. Huse, and L. Radzihovsky (World Scientific, Singapore, 2024), Chap. 14, p. 169.
  108. P. Weinberg and M. Bukov, QuSpin: A Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  109. L. Tagliacozzo, G. Evenbly, and G. Vidal, Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law, Phys. Rev. B 80, 235127 (2009).
  110. Introduction to Tensor Network Methods: From Many-body Quantum Systems to Machine Learning, edited by T. Felser and S. Montangero, Graduate Texts in Physics (Springer, Cham, 2026).
  111. L. Kohn, P. Silvi, M. Gerster, M. Keck, R. Fazio, G. E. Santoro, and S. Montangero, Superfluid-to-Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation, Phys. Rev. A 101, 023617 (2020).
  112. F. Baccari, D. Bacilieri, M. Ballarin, F. P. Barone, F. Campaioli, A. G. Catalano, G. Cataldi, M. Colombo, A. Coppi, A. Costantini, A. Datta, A. De Girolamo, D. Jaschke, S. B. Kožić, G. Magnifico, C. Mordini, S. Montangero, M. Menon, G. Muñoz Menés, S. Notarnicola, et al., Quantum TEA: qtealeaves (Version 1.12.5) [Computer software], Zenodo, 2026, https://doi.org/10.5281/zenodo.20109357.
  113. F. Baccari, M. Ballarin, F. P. Barone, A. Coppi, A. De Girolamo, D. Jaschke, S. Montangero, C. Mordini, L. Pavešić, D. Rattacaso, and N. Reinić, Quantum TEA: qredtea (Version 0.2.0) [Computer software], Zenodo, 2025, https://doi.org/10.5281/zenodo.14883296.
  114. D. Jaschke, M. Ballarin, N. Reinić, L. Pavešić, and S. Montangero, Benchmarking quantum red TEA on CPUs, GPUs, and TPUs, in Proceedings of the 10th bwHPC Symposium: HPC Activities in Baden-Württemberg (KIT Scientific Publishing, Karlsruhe, 2024), p. 45.

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Phys. Rev. B 114, 225126– Published 15 October, 2026
  • Received 27 January 2026
  • Revised 14 September 2026
  • Accepted 17 September 2026
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