Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
133 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Renormalization group of topological scattering networks (2404.15866v1)

Published 24 Apr 2024 in cond-mat.dis-nn and physics.comp-ph

Abstract: Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space renormalization group (RG) approach for scattering models, which is capable of dealing with strong distributed disorder without relying on the renormalization of Hamiltonians or wave functions. Such scheme, based on a block-scattering transformation combined with a replica strategy, is applied for a comprehensive study of strongly disordered unitary scattering networks with localized bulk states, uncovering a connection between topological physics and critical behavior. Our RG scheme leads to topological flow diagrams that unveil how the microscopic competition between reflection and non-reciprocity leads to the large-scale emergence of macroscopic scattering attractors, corresponding to trivial and topological insulators. Our findings are confirmed by a scaling analysis of the localization length (LL) and critical exponents, and experimentally validated. The results not only shed light on the fundamental understanding of topological phase transitions and scaling properties in strongly disordered regimes, but also pave the way for practical applications in modern topological condensed-matter and photonics, where disorder may be seen as a useful design degree of freedom, and no longer as a hindrance.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (62)
  1. D. Stauffer, Scaling theory of percolation clusters, Physics Reports 54, 1 (1979).
  2. B. Shapiro, Renormalization-Group Transformation for the Anderson Transition, Physical Review Letters 48, 823 (1982).
  3. B. Huckestein, Scaling theory of the integer quantum Hall effect, Reviews of Modern Physics 67, 357 (1995), publisher: American Physical Society.
  4. H. A. Fertig, Semiclassical description of a two-dimensional electron in a strong magnetic field and an external potential, Physical Review B 38, 996 (1988).
  5. J. Cardy, Network Models in Class C on Arbitrary Graphs, Communications in Mathematical Physics 258, 87 (2005).
  6. B. Kramer, T. Ohtsuki, and S. Kettemann, Random network models and quantum phase transitions in two dimensions, Physics Reports 417, 211 (2005).
  7. J. T. Chalker and P. D. Coddington, Percolation, quantum tunnelling and the integer Hall effect, Journal of Physics C: Solid State Physics 21, 2665 (1988).
  8. K. Slevin and T. Ohtsuki, Critical exponent for the quantum Hall transition, Physical Review B 80, 041304 (2009).
  9. M. Pasek and Y. D. Chong, Network models of photonic Floquet topological insulators, Physical Review B 89, 075113 (2014).
  10. P. Delplace, M. Fruchart, and C. Tauber, Phase rotation symmetry and the topology of oriented scattering networks, Physical Review B 95, 205413 (2017).
  11. Z. Zhang, P. Delplace, and R. Fleury, Superior robustness of anomalous non-reciprocal topological edge states, Nature 598, 293 (2021).
  12. G. Q. Liang and Y. D. Chong, Optical Resonator Analog of a Two-Dimensional Topological Insulator, Physical Review Letters 110, 203904 (2013).
  13. H. Liu, I. C. Fulga, and J. K. Asbóth, Anomalous levitation and annihilation in Floquet topological insulators, Physical Review Research 2, 022048 (2020).
  14. A. C. Potter, J. Chalker, and V. Gurarie, Quantum Hall Network Models as Floquet Topological Insulators, Physical Review Letters 125, 086601 (2020).
  15. Z. Zhang, P. Delplace, and R. Fleury, Anomalous topological waves in strongly amorphous scattering networks, Science Advances 9, eadg3186 (2023).
  16. J. Shapiro and C. Tauber, Strongly Disordered Floquet Topological Systems, Annales Henri Poincaré 20, 1837 (2019), arXiv:1807.03251 [cond-mat, physics:math-ph].
  17. G. M. Graf and C. Tauber, Bulk–Edge Correspondence for Two-Dimensional Floquet Topological Insulators, Annales Henri Poincaré 19, 709 (2018).
  18. E. Prodan, Disordered Topological Insulators: A Non-Commutative Geometry Perspective, Journal of Physics A: Mathematical and Theoretical 44, 113001 (2011), arXiv:1010.0595 [cond-mat, physics:math-ph].
  19. K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Reviews of Modern Physics 47, 773 (1975), publisher: American Physical Society.
  20. M. E. Fisher, Renormalization group theory: Its basis and formulation in statistical physics, Reviews of Modern Physics 70, 653 (1998), publisher: American Physical Society.
  21. J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, 1996).
  22. D. P. Arovas, M. Janssen, and B. Shapiro, Real-space renormalization of the Chalker-Coddington model, Physical Review B 56, 4751 (1997), publisher: American Physical Society.
  23. P. Cain, M. E. Raikh, and R. A. Römer, Real-Space Renormalization Group Approach to the Quantum Hall Transition, Journal of the Physical Society of Japan 72, 135 (2003).
  24. M. Janssen, R. Merkt, and A. Weymer, S-matrix network models for coherent waves in random media: construction and renormalization, Annalen der Physik 510, 353 (1998).
  25. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, Journal of Physics C: Solid State Physics 6, 1181 (1973).
  26. Z.-C. Gu and X.-G. Wen, Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order, Physical Review B 80, 155131 (2009).
  27. T. Morimoto, A. Furusaki, and C. Mudry, Anderson localization and the topology of classifying spaces, Physical Review B 91, 235111 (2015).
  28. W. Chen, Scaling theory of topological phase transitions, Journal of Physics: Condensed Matter 28, 055601 (2016).
  29. R. S. K. Mong, J. H. Bardarson, and J. E. Moore, Quantum Transport and Two-Parameter Scaling at the Surface of a Weak Topological Insulator, Physical Review Letters 108, 076804 (2012).
  30. E. Prodan and H. Schulz-Baldes, Non-commutative odd Chern numbers and topological phases of disordered chiral systems, Journal of Functional Analysis 271, 1150 (2016).
  31. C. Guo and S. Fan, Reciprocity Constraints on Reflection, Physical Review Letters 128, 256101 (2022).
  32. Z. Zhang, Topological photonic transport in disordered scattering networks, Ph.D. thesis, EPFL.
  33. Q. Marsal, D. Varjas, and A. G. Grushin, Topological Weaire–Thorpe models of amorphous matter, Proceedings of the National Academy of Sciences 117, 30260 (2020).
  34. A. G. Grushin and C. Repellin, Amorphous and Polycrystalline Routes toward a Chiral Spin Liquid, Physical Review Letters 130, 186702 (2023).
  35. I. C. Fulga, F. Hassler, and A. R. Akhmerov, Scattering theory of topological insulators and superconductors, Physical Review B 85, 165409 (2012), publisher: American Physical Society.
  36. M. Büttiker, Four-Terminal Phase-Coherent Conductance, Physical Review Letters 57, 1761 (1986).
  37. S. Rotter and S. Gigan, Light fields in complex media: Mesoscopic scattering meets wave control, Reviews of Modern Physics 89, 015005 (2017).
  38. F. D. Murnaghan, The Orthogonal and Symplectic Groups, Communications of the Dublin Institute for Advanced Studies  (1958).
  39. P. Dita, On the parametrisation of unitary matrices by the moduli of their elements, Communications in Mathematical Physics 159, 581 (1994).
  40. P. Dita, Factorization of Unitary Matrices (2001), arXiv:math-ph/0103005.
  41. L.-L. Chau and W.-Y. Keung, Comments on the Parametrization of the Kobayashi-Maskawa Matrix, Physical Review Letters 53, 1802 (1984).
  42. P. Diţă, Separation of unistochastic matrices from the double stochastic ones: Recovery of a 3×3 unitary matrix from experimental data, Journal of Mathematical Physics 47, 083510 (2006).
  43. A. Altland, A. Kamenev, and C. Tian, Anderson Localization from the Replica Formalism, Physical Review Letters 95, 206601 (2005).
  44. G. Parisi, On the replica approach to glasses (1997), arXiv:cond-mat/9701068.
  45. G. Parisi, The physical Meaning of Replica Symmetry Breaking (2002), arXiv:cond-mat/0205387.
  46. M. Castellana, The Renormalization Group for Disordered Systems (2013), arXiv:1307.6891 [cond-mat].
  47. M. C. Angelini and G. Biroli, Real space renormalization group theory of disordered models of glasses, Proceedings of the National Academy of Sciences 114, 3328 (2017), publisher: Proceedings of the National Academy of Sciences.
  48. A. G. Galstyan and M. E. Raikh, Localization and conductance fluctuations in the integer quantum Hall effect: Real-space renormalization-group approach, Physical Review B 56, 1422 (1997).
  49. R. Klesse and M. Metzler, Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect, Physical Review Letters 79, 721 (1997).
  50. M. Metzler, The Influence of Percolation in the generalized Chalker-Coddington Model, Journal of the Physical Society of Japan 68, 144 (1999), arXiv:cond-mat/9809285.
  51. R. Merkt, M. Janssen, and B. Huckestein, Network model for a two-dimensional disordered electron system with spin-orbit scattering, Physical Review B 58, 4394 (1998).
  52. M. Onoda, Y. Avishai, and N. Nagaosa, Localization in a Quantum Spin Hall System, Physical Review Letters 98, 076802 (2007), publisher: American Physical Society.
  53. S. Liu, T. Ohtsuki, and R. Shindou, Effect of Disorder in a Three-Dimensional Layered Chern Insulator, Physical Review Letters 116, 066401 (2016).
  54. A. MacKinnon and B. Kramer, MacKinnon and Kramer Respond, Physical Review Letters 49, 695 (1982).
  55. J. H. Son and S. Raghu, 3D Network Model for Strong Topological Insulator Transitions, Physical Review B 104, 125142 (2021), arXiv:2008.03315 [cond-mat].
  56. S. Munshi and R. Yang, Self-adjoint elements in the pseudo-unitary group U(p,p), Linear Algebra and its Applications 560, 100 (2019).
  57. K. Slevin and T. Ohtsuki, Critical exponent for the Anderson transition in the three-dimensional orthogonal universality class, New Journal of Physics 16, 015012 (2014).
  58. A. MacKinnon and B. Kramer, One-Parameter Scaling of Localization Length and Conductance in Disordered Systems, Physical Review Letters 47, 1546 (1981).
  59. K. Slevin and T. Ohtsuki, Corrections to Scaling at the Anderson Transition, Physical Review Letters 82, 382 (1999).
  60. A. Agarwala and V. B. Shenoy, Topological Insulators in Amorphous Systems, Physical Review Letters 118, 236402 (2017).
  61. M. S. Rudner and N. H. Lindner, Band structure engineering and non-equilibrium dynamics in Floquet topological insulators, Nature Reviews Physics 2, 229 (2020).
  62. N. H. Lindner, G. Refael, and V. Galitski, Floquet topological insulator in semiconductor quantum wells, Nature Physics 7, 490 (2011).

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets