Observation of critical topological phase transition

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References

  1. Landau, L. D. & Lifshitz, E. M. Statistical Physics Vol. 5 https://doi.org/10.1016/C2009-0-24487-4 (Elsevier, 1980).

  2. Sachdev, S. Quantum Phase Transitions 2nd edn https://doi.org/10.1017/CBO9780511973765 (Cambridge Univ. Press, 2011).

  3. Osterloh, A., Amico, L., Falci, G. & Fazio, R. Scaling of entanglement close to a quantum phase transition. Nature 416, 608 (2002).

    Article  CAS  PubMed  Google Scholar 

  4. Haldane, F. D. M. Nobel lecture: topological quantum matter. Rev. Mod. Phys. 89, 040502 (2017).

    Article  MathSciNet  Google Scholar 

  5. Kosterlitz, J. M. Nobel lecture: topological defects and phase transitions. Rev. Mod. Phys. 89, 040501 (2017).

    Article  MathSciNet  Google Scholar 

  6. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010).

    Article  CAS  Google Scholar 

  7. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).

    Article  CAS  Google Scholar 

  8. Senthil, T. Symmetry-protected topological phases of quantum matter. Annu. Rev. Condens. Matter Phys. 6, 299 (2015).

    Article  CAS  Google Scholar 

  9. Wen, X.-G. Colloquium: zoo of quantum-topological phases of matter. Rev. Mod. Phys. 89, 041004 (2017).

    Article  MathSciNet  Google Scholar 

  10. Scaffidi, T., Parker, D. E. & Vasseur, R. Gapless symmetry-protected topological order. Phys. Rev. X 7, 041048 (2017).

    Google Scholar 

  11. Verresen, R., Jones, N. G. & Pollmann, F. Topology and edge modes in quantum critical chains. Phys. Rev. Lett. 120, 057001 (2018).

    Article  CAS  PubMed  Google Scholar 

  12. Verresen, R., Thorngren, R., Jones, N. G. & Pollmann, F. Gapless topological phases and symmetry-enriched quantum criticality. Phys. Rev. X 11, 041059 (2021).

    CAS  Google Scholar 

  13. Yu, X.-J. et al. Conformal boundary conditions of symmetry-enriched quantum critical spin chains. Phys. Rev. Lett. 129, 210601 (2022).

    Article  CAS  PubMed  Google Scholar 

  14. Yu, X.-J., Xu, L. & Lin, H.-Q. Topological physics in quantum critical systems. Phys. Rep. 1160, 1 (2026).

    Article  MathSciNet  Google Scholar 

  15. Calabrese, P. & Cardy, J. Entanglement entropy and quantum field theory. J. Stat. Mech. 2004, P06002 (2004).

    Article  Google Scholar 

  16. Kokail, C., van Bijnen, R., Elben, A., Vermersch, B. & Zoller, P. Entanglement Hamiltonian tomography in quantum simulation. Nat. Phys. 17, 936 (2021).

    Article  CAS  Google Scholar 

  17. Joshi, M. K. et al. Exploring large-scale entanglement in quantum simulation. Nature 624, 539 (2023).

    Article  CAS  PubMed  Google Scholar 

  18. Verresen, R., Moessner, R. & Pollmann, F. One-dimensional symmetry protected topological phases and their transitions. Phys. Rev. B 96, 165124 (2017).

    Article  Google Scholar 

  19. Verresen, R. Topology and edge states survive quantum criticality between topological insulators. Preprint at https://arxiv.org/abs/2003.05453 (2020).

  20. Thorngren, R., Vishwanath, A. & Verresen, R. Intrinsically gapless topological phases. Phys. Rev. B 104, 075132 (2021).

    Article  CAS  Google Scholar 

  21. Wen, R. & Potter, A. C. Bulk-boundary correspondence for intrinsically gapless symmetry-protected topological phases from group cohomology. Phys. Rev. B 107, 245127 (2023).

    Article  CAS  Google Scholar 

  22. Li, L., Oshikawa, M. & Zheng, Y. Intrinsically/purely gapless-SPT from non-invertible duality transformations. SciPost Phys. 18, 153 (2025).

  23. Wen, R. & Potter, A. C. Classification of 1+1D gapless symmetry protected phases via topological holography. Phys. Rev. B 111, 115161 (2025).

  24. Huang, S.-J. & Cheng, M. Topological holography, quantum criticality, and boundary states. SciPost Phys. 18, 213 (2025).

  25. Li, L., Oshikawa, M. & Zheng, Y. Decorated defect construction of gapless-SPT states. SciPost Phys. 17, 013 (2024).

    Article  MathSciNet  Google Scholar 

  26. Yu, X.-J., Yang, S., Lin, H.-Q. & Jian, S.-K. Universal entanglement spectrum in one-dimensional gapless symmetry protected topological states. Phys. Rev. Lett. 133, 026601 (2024).

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  27. Yu, X.-J. & Li, W.-L. Fidelity susceptibility at the Lifshitz transition between the noninteracting topologically distinct quantum critical points. Phys. Rev. B 110, 045119 (2024).

    Article  Google Scholar 

  28. Zhong, W.-H., Li, W.-L., Chen, Y.-C. & Yu, X.-J. Topological edge modes and phase transitions in a critical fermionic chain with long-range interactions. Phys. Rev. A 110, 022212 (2024).

    Article  MathSciNet  CAS  Google Scholar 

  29. Zhang, H.-L., Li, H.-Z., Yang, S. & Yu, X.-J. Quantum phase transition and critical behavior between the gapless topological phases. Phys. Rev. A 109, 062226 (2024).

    Article  CAS  Google Scholar 

  30. Yang, S., Lin, H.-Q. & Yu, X.-J. Gapless topological behaviors in a long-range quantum spin chain. Commun. Phys. 8, 27 (2025).

    Article  CAS  Google Scholar 

  31. Yu, X.-J., Yang, S., Liu, S., Lin, H.-Q. & Jian, S.-K. Gapless symmetry-protected topological states in measurement-only circuits. Phys. Rev. B 113, 134302 (2026).

  32. Yang, S. et al. Deconfined criticality as intrinsically gapless topological state in one dimension. Phys. Rev. B 113, L201105 (2026).

  33. Flores-Calderón, R., König, E. J. & Cook, A. M. Topological quantum criticality from multiplicative topological phases. Phys. Rev. Lett. 134, 116602 (2025).

    Article  PubMed  Google Scholar 

  34. Tan, Z. et al. Exploring nontrivial topology at quantum criticality on a superconducting processor. Commun. Phys. 9, 136 (2026).

  35. Zhou, L., Zhang, F. & Pan, J. Floquet Möbius topological insulators. Phys. Rev. B 112, 134302 (2025).

    Article  CAS  Google Scholar 

  36. Kumar, R. R., Kartik, Y., Rahul, S. & Sarkar, S. Multi-critical topological transition at quantum criticality. Sci. Rep. 11, 1004 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Sarkar, S. Topological transition on a conformal manifold for the quantum Ising model with a longer range interaction. Sci. Rep. 15, 5916 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Zhou, L., Wang, R. & Pan, J. Gapless higher-order topology and corner states in Floquet systems. Phys. Rev. Res. 7, 023079 (2025).

    Article  CAS  Google Scholar 

  39. Kirschbaum, D. et al. Emergent topological semimetal from quantum criticality. Nat. Phys. 22, 218 (2026).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Zhou, L., Gong, J. & Yu, X.-J. Topological edge states at Floquet quantum criticality. Commun. Phys. 8, 214 (2025).

    Article  Google Scholar 

  41. Liu, H. et al. Acoustic topological metamaterials of large winding number. Phys. Rev. Appl. 19, 054028 (2023).

    Article  CAS  Google Scholar 

  42. Rajabpoor Alisepahi, A., Sarkar, S., Sun, K. & Ma, J. Breakdown of conventional winding number calculation in one-dimensional lattices with interactions beyond nearest neighbors. Commun. Phys. 6, 334 (2023).

    Article  Google Scholar 

  43. Chen, Y., Fleury, R., Seppecher, P., Hu, G. & Wegener, M. Nonlocal metamaterials and metasurfaces. Nat. Rev. Phys. 7, 299 (2025).

    Article  Google Scholar 

  44. Zhu, W., Xue, H., Gong, J., Chong, Y. & Zhang, B. Time-periodic corner states from Floquet higher-order topology. Nat. Commun. 13, 11 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Cheng, Z. et al. Observation of π/2 modes in an acoustic Floquet system. Phys. Rev. Lett. 129, 254301 (2022).

    Article  CAS  PubMed  Google Scholar 

  46. Tong, Q.-J., An, J.-H., Gong, J., Luo, H.-G. & Oh, C. H. Generating many Majorana modes via periodic driving: a superconductor model. Phys. Rev. B 87, 201109(R) (2013).

    Article  Google Scholar 

  47. Asbóth, J. K. & Obuse, H. Bulk-boundary correspondence for chiral symmetric quantum walks. Phys. Rev. B 88, 121406(R) (2013).

    Article  Google Scholar 

  48. Coulais, C., Kettenis, C. & van Hecke, M. A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials. Nat. Phys. 14, 40 (2018).

    Article  CAS  Google Scholar 

  49. Chen, Y. et al. Anomalous frozen evanescent phonons. Nat. Commun. 15, 8882 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  MathSciNet  CAS  Google Scholar 

  51. Zhang, D.-W., Zhu, Y.-Q., Zhao, Y. X., Yan, H. & Zhu, S.-L. Topological quantum matter with cold atoms. Adv. Phys. 67, 253 (2018).

    Article  Google Scholar 

  52. Cardoso, G., Yeh, H.-C., Korneev, L., Abanov, A. G. & Mitra, A. Gapless Floquet topology. Phys. Rev. B 111, 125162 (2025).

    Article  CAS  Google Scholar 

  53. Xue, H., Yang, Y. & Zhang, B. Topological acoustics. Nat. Rev. Mater. 7, 974 (2022).

    Article  Google Scholar 

  54. Chen, L.-M., Zhou, Y., Chen, S. A. & Ye, P. Quantum entanglement and non-Hermiticity in free-fermion systems. Chin. Phys. Lett. 41, 127302 (2024).

    Article  Google Scholar 

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