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Multipartite quantum nonlocality and topological quantum phase transitions in a spin-1/2 two-leg Kitaev ladder

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Abstract

Multipartite nonlocality, a measure of multipartite quantum correlations, is used to characterize topological quantum phase transitions (QPTs) in an infinite-size spin-1/2 two-leg Kitaev ladder model. First of all, the nonlocality measure \({\mathcal {S}}\) is singular at the critical points, thus these topological QPTs are accompanied by dramatic changes of multipartite quantum correlations. The influence of the inter-chain coupling upon multipartite nonlocality is also investigated. Furthermore, we carry out scaling analysis and find that the logarithm measure scales linearly as \(\log _2{\mathcal {S}}_n \sim {\mathcal {K}} n +b\), with n the length of the concerned subchain. It is clear that the slope \({\mathcal {K}}\) plays a central role in the large-n behavior of the nonlocality in the ladder. Especially, as n increases, we find the finite-size slope \({\mathcal {K}}_n\) converges slowly in the \(\varDelta _{x,y}\) phases which present non-local string orders, and quite rapidly in the \(\varDelta _0\) phase which does not present any string order. We figure out a clear picture to explain these different behaviors.

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Notes

  1. Here we have added a constant factor \(\frac{1}{2}\), so that the two-qubit operator \({\hat{S}}_2\) in Eq. (2) and multi-qubit operator \({\hat{S}}_n\) in Eq. (4) can be expressed in a unified way.

References

  1. O. Gühne, G. Töth, H.J. Briegel, New J. Phys. 7, 229 (2005)

    Article  Google Scholar 

  2. F. Levi, F. Mintert, Phys. Rev. Lett. 110, 150402 (2013)

    Article  ADS  Google Scholar 

  3. M. Paternostro, D. Vitali, S. Gigan, M.S. Kim, C. Brukner, J. Eisert, M. Aspelmeyer, Phys. Rev. Lett. 99, 250401 (2007)

    Article  ADS  Google Scholar 

  4. D. Collins, N. Gisin, S. Popescu, D. Roberts, V. Scarani, Phys. Rev. Lett. 88, 170405 (2002)

    Article  ADS  Google Scholar 

  5. Q.Y. He, E.G. Cavalcanti, M.D. Reid, P.D. Drummond, Phys. Rev. Lett. 103, 180402 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  6. J.D. Bancal, C. Branciard, N. Gisin, S. Pironio, Phys. Rev. Lett. 103, 090503 (2009)

    Article  ADS  Google Scholar 

  7. J. Batle, M. Casas, J. Phys. A Math. Theor. 44, 445304 (2011)

    Article  ADS  Google Scholar 

  8. N. Brunner, J. Sharam, T. Vértesi, Phys. Rev. Lett. 108, 110501 (2012)

    Article  ADS  Google Scholar 

  9. X. Wang, C. Zhang, Q. Chen, S. Yu, H. Yuan, C.H. Oh, Phys. Rev. A 94, 022110 (2016)

    Article  ADS  Google Scholar 

  10. J. Bowles, J. Francfort, M. Fillettaz, F. Hirsch, N. Brunner, Phys. Rev. Lett. 116, 130401 (2016)

    Article  ADS  Google Scholar 

  11. J.D. Bancal, J. Barrett, N. Gisin, S. Pironio, Phys. Rev. A 88, 014102 (2013)

    Article  ADS  Google Scholar 

  12. G.B. Xu, Q.Y. Wen, S.J. Qin, Y.H. Yang, F. Gao, Phys. Rev. A 93, 032341 (2016)

    Article  ADS  Google Scholar 

  13. R. Orús, Ann. Phys. 349, 117 (2014)

    Article  MathSciNet  ADS  Google Scholar 

  14. U. Schollwöck, Ann. Phys. 326, 96 (2011) (January 2011 special issue)

  15. Z.Y. Sun, S. Liu, H.L. Huang, D. Zhang, Y.Y. Wu, J. Xu, B.F. Zhan, H.G. Cheng, C.B. Duan, B. Wang, Phys. Rev. A 90, 062129 (2014)

    Article  ADS  Google Scholar 

  16. Z.Y. Sun, B. Guo, H.L. Huang, Phys. Rev. A 92, 022120 (2015)

    Article  ADS  Google Scholar 

  17. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999)

    MATH  Google Scholar 

  18. Z.Y. Sun, Y.Y. Wu, J. Xu, H.L. Huang, B.F. Zhan, B. Wang, C.B. Duan, Phys. Rev. A 89, 022101 (2014)

    Article  ADS  Google Scholar 

  19. S. Campbell, M. Paternostro, Phys. Rev. A 82, 042324 (2010)

    Article  ADS  Google Scholar 

  20. J. Batle, M. Casas, Phys. Rev. A 82, 062101 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  21. Y. Dai, C. Zhang, W. You, Y. Dong, C.H. Oh, Phys. Rev. A 96, 012336 (2017)

    Article  ADS  Google Scholar 

  22. L. Justino, T.R. de Oliveira, Phys. Rev. A 85, 052128 (2012)

    Article  ADS  Google Scholar 

  23. D.L. Deng, C. Wu, J.L. Chen, S.J. Gu, S. Yu, C.H. Oh, Phys. Rev. A 86, 032305 (2012)

    Article  ADS  Google Scholar 

  24. Z.Y. Sun, M. Wang, Y.Y. Wu, B. Guo, Phys. Rev. A 99, 042323 (2019)

    Article  ADS  Google Scholar 

  25. H.G. Cheng, M. Li, Y.Y. Wu, M. Wang, D. Zhang, J. Bao, B. Guo, Z.Y. Sun, Phys. Rev. A 101, 052116 (2020)

    Article  ADS  Google Scholar 

  26. J.M. Kosterlitz, D.J. Thouless, J. Phys. C Solid State Phys. 6, 1181 (1973)

    Article  ADS  Google Scholar 

  27. J.M. Kosterlitz, Rev. Mod. Phys. 89, 040501 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  28. F.D.M. Haldane, Rev. Mod. Phys. 89, 040502 (2017)

    Article  ADS  Google Scholar 

  29. X.G. Wen, Rev. Mod. Phys. 89, 041004 (2017)

    Article  ADS  Google Scholar 

  30. W.W. Cheng, Z.Z. Du, L.Y. Gong, S.M. Zhao, J.M. Liu, Epl 108, 46003 (2014)

    Article  ADS  Google Scholar 

  31. M. Johansson, M. Ericsson, E. Sjöqvist, A. Osterloh, Phys. Rev. A 89, 012320 (2014)

    Article  ADS  Google Scholar 

  32. C.J. Shan, W.W. Cheng, J.B. Liu, Y.S. Cheng, T.K. Liu, Sci. Rep. 4, 4473 (2014)

    Article  Google Scholar 

  33. M. Greiter, V. Schnells, R. Thomale, Ann. Phys. 351, 1026 (2014)

    Article  ADS  Google Scholar 

  34. K. Kato, F. Furrer, M. Murao, Phys. Rev. A 93, 022317 (2016)

    Article  ADS  Google Scholar 

  35. R. Orús, T.C. Wei, O. Buerschaper, A. García-Saez, Phys. Rev. Lett. 113, 257202 (2014)

    Article  ADS  Google Scholar 

  36. L. Pezzè, M. Gabbrielli, L. Lepori, A. Smerzi, Phys. Rev. Lett. 119, 250401 (2017)

    Article  ADS  Google Scholar 

  37. I.N. Karnaukhov, I.O. Slieptsov, Eur. Phys. J. B 87, 230 (2014)

    Article  ADS  Google Scholar 

  38. C.K. Chiu, J.C.Y. Teo, A.P. Schnyder, S. Ryu, Rev. Mod. Phys. 88, 035005 (2016)

    Article  ADS  Google Scholar 

  39. Y.R. Zhang, Y. Zeng, H. Fan, J.Q. You, F. Nori, Phys. Rev. Lett. 120, 250501 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  40. M. den Nijs, K. Rommelse, Phys. Rev. B 40, 4709 (1989)

    Article  ADS  Google Scholar 

  41. H. Tasaki, Phys. Rev. Lett. 66, 798 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  42. H.T. Wang, B. Li, S.Y. Cho, Phys. Rev. B 87, 054402 (2013)

    Article  ADS  Google Scholar 

  43. J.H. Liu, H.T. Wang, Eur. Phys. J. B 88, 256 (2015)

    Article  ADS  Google Scholar 

  44. X.Y. Feng, G.M. Zhang, T. Xiang, Phys. Rev. Lett. 98, 087204 (2007)

    Article  ADS  Google Scholar 

  45. J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)

  46. T.R. de Oliveira, A. Saguia, M.S. Sarandy, EPL (Europhys. Lett.) 100, 60004 (2012)

    Article  Google Scholar 

  47. F. Altintas, R. Eryigit, Ann. Phys. 327, 3084 (2012)

    Article  ADS  Google Scholar 

  48. R. Horodecki, P. Horodecki, M. Horodecki, Phys. Lett. A 200, 340 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  49. A. Kitaev, Ann. Phys. 321, 2 (2006) (January special issue)

  50. H.D. Chen, Z. Nussinov, J. Phys. A Math. Theor. 41, 075001 (2008)

    Article  ADS  Google Scholar 

  51. G.C. Wick, Phys. Rev. 80, 268 (1950)

    Article  MathSciNet  ADS  Google Scholar 

  52. I.P. McCulloch, M. Gulácsi, Europhys. Lett. (EPL) 57, 852 (2002)

    Article  ADS  Google Scholar 

  53. A. Koitzsch, C. Habenicht, E. Müller, M. Knupfer, B. Büchner, H.C. Kandpal, J. van den Brink, D. Nowak, A. Isaeva, T. Doert, Phys. Rev. Lett. 117, 126403 (2016)

    Article  ADS  Google Scholar 

  54. C.E. Agrapidis, J. van den Brink, S. Nishimoto, Sci. Rep. 8, 1815 (2018)

    Article  ADS  Google Scholar 

  55. A. Catuneanu, E.S. Sørensen, H.Y. Kee, Phys. Rev. B 99, 195112 (2019)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The research was supported by the National Natural Science Foundation of China (Grant No. 11675124).

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Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan, 430000, China

    Zhao-Yu Sun, Meng Li, Hui-Xin Wen, Hong-Guang Cheng, Jian Xu & Yan-Shan Chen

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  1. Zhao-Yu Sun
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Correspondence to Zhao-Yu Sun.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data generated or analyzed during this study are included in this published article.]

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Sun, ZY., Li, M., Wen, HX. et al. Multipartite quantum nonlocality and topological quantum phase transitions in a spin-1/2 two-leg Kitaev ladder. Eur. Phys. J. B 94, 141 (2021). https://doi.org/10.1140/epjb/s10051-021-00150-7

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