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Weyl-Mott point: Topological and non-Fermi liquid behavior from an isolated Green's function zero

R. Flores-Calderón1,2 and Chris Hooley3

Phys. Rev. B 111, 235139 – Published 23 June, 2025

DOI: https://doi.org/10.1103/k4st-77ph

Abstract

We present a model in which a Hatsugai-Kohmoto interaction is added to a system of fermions with a Weyl point in their noninteracting dispersion relation, and analyze its behavior as a function of the chemical potential. We show that the model exhibits a Weyl-Mott point, a single isolated Green's function zero, and that this implies a non-Fermi liquid state at the border of the metallic regime and a gapped topological state for the insulating one. The Weyl-Mott point inherits the topological charge from the original Green's function pole, and is therefore naturally associated with a strongly correlated chiral anomaly.

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References (65)

  1. M. Levin and A. Stern, Fractional topological insulators, Phys. Rev. Lett. 103, 196803 (2009).
  2. B. Swingle, Entanglement entropy and the Fermi surface, Phys. Rev. Lett. 105, 050502 (2010).
  3. D. Schuricht, F.H.L. Essler, A. Jaefari, and E. Fradkin, Topological order in a three-dimensional system of strongly interacting photons, Phys. Rev. B 83, 035111 (2011).
  4. T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106, 236804 (2011).
  5. L. Santos, T. Neupert, S. Ryu, C. Chamon, and C. Mudry, Topological phase transitions in the spin-orbit coupled electron gas, Phys. Rev. B 84, 165138 (2011).
  6. M. Levin and A. Stern, Exactly soluble models for fractional topological insulators in two dimensions, Phys. Rev. B 84, 235145 (2011).
  7. M. Levin, Protected edge modes without symmetry, Phys. Rev. X 3, 021009 (2013).
  8. X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry protected topological orders in interacting bosonic systems, Science 338, 1604 (2012).
  9. Z.-C. Gu and X.-G. Wen, Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear sigma models and a special group supercohomology theory, Phys. Rev. B 90, 115141 (2014).
  10. A. Vishwanath and T. Senthil, Three-dimensional bosonic topological insulator: Symmetry-protected topological order, and the boundary degrees of freedom, Phys. Rev. X 3, 011016 (2013).
  11. C. Wang and T. Senthil, Boson topological insulators: A window into highly entangled quantum phases, Phys. Rev. B 87, 235122 (2013).
  12. F. J. Burnell, X. Chen, L. Fidkowski, and A. Vishwanath, Exactly solvable model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order, Phys. Rev. B 90, 245122 (2014).
  13. A. Kapustin, Symmetry protected topological phases, anomalies, and cobordisms: Beyond group cohomology, arXiv:1403.1467.
  14. L. Fidkowski, X. Chen, and A. Vishwanath, Non-abelian topological order on the surface of a 3D topological superconductor from an exactly solved model, Phys. Rev. X 3, 041016 (2013).
  15. C. Wang and T. Senthil, Interacting fermionic topological insulators/superconductors in three dimensions, Phys. Rev. B 89, 195124 (2014).
  16. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Topological insulators in three dimensions, Nature (London) 452, 970 (2008).
  17. C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
  18. C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005).
  19. L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98, 106803 (2007).
  20. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Classification of topological insulators and superconductors, Phys. Rev. B 78, 195125 (2008).
  21. J. E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75, 121306(R) (2007).
  22. F. D. M. Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model, Phys. Lett. A 93, 464 (1983).
  23. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Valence bond ground states in isotropic quantum antiferromagnets, Commun. Math. Phys. 115, 477 (1988).
  24. X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems, Phys. Rev. B 83, 035107 (2011).
  25. T. Senthil, Symmetry-protected topological phases of quantum matter, Annu. Rev. Condens. Matter Phys. 6, 299 (2015).
  26. R. Verresen, R. Moessner, and F. Pollmann, One-dimensional symmetry protected topological phases and their transitions, Phys. Rev. B 96, 165124 (2017).
  27. R. Verresen, N. G. Jones, and F. Pollmann, Topology and edge modes in quantum critical chains, Phys. Rev. Lett. 120, 057001 (2018).
  28. T. Scaffidi, D. E. Parker, and R. Vasseur, Gapless symmetry-protected topological order, Phys. Rev. X 7, 041048 (2017).
  29. R. Thorngren, A. Vishwanath, and R. Verresen, Intrinsically gapless topological phases, Phys. Rev. B 104, 075132 (2021).
  30. R. Verresen, U. Borla, A. Vishwanath, S. Moroz, and R. Thorngren, Higgs condensates are symmetry-protected topological phases: I. Discrete symmetries, arXiv:2211.01376.
  31. K. T. K. Chung, R. Flores-Calderón, R. C. Torres, P. Ribeiro, S. Moroz, and P. McClarty, Higgs phases and boundary criticality, arXiv:2404.17001.
  32. L. Peralta Gavensky, S. Sachdev, and N. Goldman, Connecting the many-body chern number to Luttinger's theorem through Streda's formula, Phys. Rev. Lett. 131, 236601 (2023).
  33. P. Mai, B. E. Feldman, and P. W. Phillips, Topological mott insulator at quarter filling in the interacting haldane model, Phys. Rev. Res. 5, 013162 (2023).
  34. S. Bollmann, C. Setty, U. F. P. Seifert, and E. J. König, Topological Green's function zeros in an exactly solved model and beyond, Phys. Rev. Lett. 133, 136504 (2024).
  35. N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. König, T. Schäfer, D. Di Sante, J. Cano, A. Millis, A. Georges, and G. Sangiovanni, Mott insulators with boundary zeros, Nat. Commun. 14, 7531 (2023).
  36. C. Setty, F. Xie, S. Sur, L. Chen, M. G. Vergniory, and Q. Si, Electronic properties, correlated topology and Green's function zeros, Phys. Rev. Res. 6, 033235 (2024).
  37. C. Setty, S. Sur, L. Chen, F. Xie, H. Hu, S. Paschen, J. Cano, and Q. Si, Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros, Phys. Rev. Res. 6, L032018 (2024).
  38. A. Blason and M. Fabrizio, Unified role of Green's function poles and zeros in correlated topological insulators, Phys. Rev. B 108, 125115 (2023).
  39. A. M. Essin and V. Gurarie, Bulk-boundary correspondence of topological insulators from their respective Green's functions, Phys. Rev. B 84, 125132 (2011).
  40. V. Gurarie, Single-particle green's functions and interacting topological insulators, Phys. Rev. B 83, 085426 (2011).
  41. J. Skolimowski and M. Fabrizio, Luttinger's theorem in the presence of Luttinger surfaces, Phys. Rev. B 106, 045109 (2022).
  42. Y. Hatsugai and M. Kohmoto, Exactly solvable model of correlated lattice electrons in any dimensions, J. Phys. Soc. Jpn. 61, 2056 (1992).
  43. P. W. Phillips, L. Yeo, and E. W. Huang, Exact theory for superconductivity in a doped Mott insulator, Nat. Phys. 16, 1175 (2020).
  44. J. Zhao, G. La Nave, and P. Phillips, Proof of a stable fixed point for strongly correlated electron matter, arXiv:2304.04787.
  45. E. W. Huang, G. L. Nave, and P. W. Phillips, Discrete symmetry breaking defines the Mott quartic fixed point, Nat. Phys. 18, 511 (2022).
  46. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  47. Z. Wang and S.-C. Zhang, Chiral anomaly, charge density waves, and axion strings from Weyl semimetals, Phys. Rev. B 87, 161107(R) (2013).
  48. A. A. Zyuzin and A. A. Burkov, Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B 86, 115133 (2012).
  49. D. Sehayek, M. Thakurathi, and A. A. Burkov, Charge density waves in Weyl semimetals, Phys. Rev. B 102, 115159 (2020).
  50. L. Crippa, A. Amaricci, N. Wagner, G. Sangiovanni, J. C. Budich, and M. Capone, Nonlocal annihilation of Weyl fermions in correlated systems, Phys. Rev. Res. 2, 012023(R) (2020).
  51. E. Bobrow, C. Sun, and Y. Li, Monopole charge density wave states in Weyl semimetals, Phys. Rev. Res. 2, 012078(R) (2020).
  52. W. Shi, B. J. Wieder, H. L. Meyerheim, Y. Sun, Y. Zhang, Y. Li, L. Shen, Y. Qi, L. Yang, J. Jena, P. Werner, K. Koepernik, S. Parkin, Y. Chen, C. Felser, B. A. Bernevig, and Z. Wang, A charge-density-wave topological semimetal, Nat. Phys. 17, 381 (2021).
  53. D. M. Kirschbaum, M. Lužnik, G. L. Roy, and S. Paschen, How to identify and characterize strongly correlated topological semimetals J. Phys. Mater. 7, 012003 (2024).
  54. H. Hu, L. Chen, C. Setty, M. Garcia-Diez, S. E. Grefe, A. Prokofiev, S. Kirchner, M. G. Vergniory, S. Paschen, J. Cano, and Q. Si, Topological semimetals without quasiparticles, arXiv:2110.06182.
  55. T. Morimoto and N. Nagaosa, Weyl Mott insulator, Sci. Rep. 6, 19853 (2016).
  56. M.-F. Yang, Manifestation of topological behaviors in interacting Weyl systems: One-body versus two-body correlations, Phys. Rev. B 100, 245137 (2019).
  57. T. Meng and J. C. Budich, Unpaired Weyl nodes from long-ranged interactions: Fate of quantum anomalies, Phys. Rev. Lett. 122, 046402 (2019).
  58. D. Guerci, G. Sangiovanni, A. J. Millis, and M. Fabrizio, Electrical transport in the Hatsugai-Kohmoto model, Phys. Rev. B 111, 075124 (2025).
  59. G. G. Blesio, L. O. Manuel, P. Roura-Bas, and A. A. Aligia, Topological quantum phase transition between fermi liquid phases in an anderson impurity model, Phys. Rev. B 98, 195435 (2018).
  60. R. Žitko, G. G. Blesio, L. O. Manuel, and A. A. Aligia, Iron phthalocyanine on Au(111) is a “non-Landau” Fermi liquid, Nat. Commun. 12, 6027 (2021).
  61. S. Kundu and D. Sénéchal, Spin density wave order in interacting type-I and type-II Weyl semimetals, Phys. Rev. B 103, 085136 (2021).
  62. G. Y. Cho, C.-T. Hsieh, and S. Ryu, Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases, Phys. Rev. B 96, 195105 (2017).
  63. M. Cheng and N. Seiberg, Lieb-Schultz-Mattis, Luttinger, and 't Hooft - anomaly matching in lattice systems, SciPost Phys. 15, 051 (2023).
  64. K. Fujikawa, Path-integral measure for gauge-invariant fermion theories, Phys. Rev. Lett. 42, 1195 (1979).
  65. J. Yi, X. Ying, L. Gioia, and A. A. Burkov, Topological order in interacting semimetals, Phys. Rev. B 107, 115147 (2023).

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