Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 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

Crystalline invariants of fractional Chern insulators (2405.17431v2)

Published 27 May 2024 in cond-mat.str-el, cond-mat.mes-hall, hep-th, and quant-ph

Abstract: In the presence of crystalline symmetry, topologically ordered states can acquire a host of symmetry-protected invariants. These determine the patterns of crystalline symmetry fractionalization of the anyons in addition to fractionally quantized responses to lattice defects. Here we show how ground state expectation values of partial rotations centered at high symmetry points can be used to extract crystalline invariants. Using methods from conformal field theory and G-crossed braided tensor categories, we develop a theory of invariants obtained from partial rotations, which apply to both Abelian and non-Abelian topological orders. We then perform numerical Monte Carlo calculations for projected parton wave functions of fractional Chern insulators, demonstrating remarkable agreement between theory and numerics. For the topological orders we consider, we show that the Hall conductivity, filling fraction, and partial rotation invariants fully characterize the crystalline invariants of the system. Our results also yield invariants of continuum fractional quantum Hall states protected by spatial rotational symmetry.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (40)
  1. X.-G. Wen, Physical Review B 65, 165113 (2002).
  2. X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford Univ. Press, Oxford, 2004).
  3. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
  4. M. Barkeshli and X.-L. Qi, Phys. Rev. X 2, 031013 (2012), arXiv:1112.3311 .
  5. A. M. Essin and M. Hermele, Phys. Rev. B 87, 104406 (2013).
  6. A. M. Essin and M. Hermele, Phys. Rev. B 90, 121102 (2014).
  7. Y. Ando and L. Fu, Annu. Rev. Condens. Matter Phys. 6, 361 (2015).
  8. M. Hermele and X. Chen, Phys. Rev. X 6, 041006 (2016).
  9. R. Thorngren and D. V. Else, Phys. Rev. X 8, 011040 (2018).
  10. N. Manjunath and M. Barkeshli, Phys. Rev. Research 3, 013040 (2021).
  11. N. Manjunath and M. Barkeshli, “Classification of fractional quantum hall states with spatial symmetries,”  (2020), arXiv:2012.11603 [cond-mat.str-el] .
  12. J. Herzog-Arbeitman, B. A. Bernevig,  and Z.-D. Song, “Interacting topological quantum chemistry in 2d: Many-body real space invariants,”  (2022), arXiv:2212.00030 [cond-mat.str-el] .
  13. S. Sachdev, Quantum Phases of Matter (Cambridge University Press, 2023).
  14. R. Kobayashi, Y. Zhang, Y.-Q. Wang,  and M. Barkeshli, “(2+1)d topological phases with rt symmetry: many-body invariant, classification, and higher order edge modes,”  (2024a), arXiv:2403.18887 [cond-mat.str-el] .
  15. R. A. Jalabert and S. Sachdev, Phys. Rev. B 44, 686 (1991).
  16. S. Sachdev, Reports on Progress in Physics 82, 014001 (2018).
  17. S. Sachdev and M. Vojta,   (1999), arXiv:cond-mat/9910231 [cond-mat.str-el] .
  18. Y. Qi and L. Fu, Physical Review B 91, 100401 (2015).
  19. G. Van Miert and C. Ortix, Physical Review B 97, 201111 (2018).
  20. Y. Zhang, N. Manjunath, G. Nambiar,  and M. Barkeshli, “Quantized charge polarization as a many-body invariant in (2+1)d crystalline topological states and hofstadter butterflies,”  (2022b), 2211.09127 .
  21. A. Kol and N. Read, Physical Review B 48, 8890 (1993).
  22. N. Regnault and B. A. Bernevig, Phys. Rev. X 1, 021014 (2011).
  23. D. Aasen, P. Bonderson,  and C. Knapp, “Characterization and classification of fermionic symmetry enriched topological phases,”  (2021), arXiv:2109.10911 [cond-mat.str-el] .
  24. M. Levin and X.-G. Wen, Phys. Rev. Lett. 96, 110405 (2006).
  25. A. Kitaev and J. Preskill, Physical review letters 96, 110404 (2006).
  26. Z.-P. Cian, M. Hafezi,  and M. Barkeshli, “Extracting wilson loop operators and fractional statistics from a single bulk ground state,”  (2022), arXiv:2209.14302 [cond-mat.str-el] .
  27. R. Fan, R. Sahay,  and A. Vishwanath, “Extracting the quantum hall conductance from a single bulk wavefunction,”  (2022), arXiv:2208.11710 .
  28. R. Kobayashi, T. Wang, T. Soejima, R. S. K. Mong,  and S. Ryu, “Higher hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)d topological order,”  (2024c), arXiv:2404.10814 [cond-mat.str-el] .
  29. G. Baskaran and P. W. Anderson, Physical Review B 37, 580 (1988).
  30. J. K. Jain, Physical Review B 40, 8079 (1989).
  31. X. G. Wen, Phys. Rev. Lett. 66, 802 (1991).
  32. X.-G. Wen, International journal of modern physics B 6, 1711 (1992).
  33. X.-G. Wen, Physical Review B 60, 8827 (1999).
  34. M. Barkeshli and X.-G. Wen, Physical Review B 81, 155302 (2010).
  35. V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987).
  36. X. G. Wen and A. Zee, Phys. Rev. Lett. 69, 953 (1992).
  37. D. V. Else and R. Thorngren, Phys. Rev. B 99, 115116 (2019).
  38. H. Li and F. D. M. Haldane, Phys. Rev. Lett. 101, 010504 (2008).
  39. J. I. Cirac and G. Sierra, Phys. Rev. B 81, 104431 (2010).
  40. A. Schwimmer and S. N., Physics Letter B 184, 191 (1987).
Citations (3)
View on Semantic Scholar

Summary

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

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