Abstract
We investigate the effect of Dzyaloshinskii-Moriya interaction and the anisotropy on the entanglement of the two-dimensional Heisenberg XXZ model. Concurrence and quantum Fisher information are computed to witness the entanglement. It is observed that the anisotropy suppresses the concurrence and this suppression can be compensated by the Dzyaloshinskii-Moriya interaction.We solved the model by using quantum renormalization group method and computed the unstable fixed points of the model and obtained the phase diagram of the model. In phase diagram, the critical line separates the two phases, the spinfluid phase and the N´eel phase. Interestingly, a variation in the quantum phase transition of the model is observed while tuning the Dzyaloshinskii-Moriya interaction. At phase transition point, the non analyticity using first derivative and the scaling behavior is studied for both, the concurrence and the quantum Fisher information. Moreover, the scaling exponent successfully describes the correlation length of the model at the critical point.
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References
Sachdev, S.: Quantum phase transitions. Cambridge University Press, Cambridge (1999)
Vojta, T.: Quantum phase transitions. In: Computational statistical physics (Springer, Berlin, Heidelberg) (2002)
Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum communication. Cambridge University Press, Cambridge (2000)
Osborne, T.J., Nielsen, M.A.: ., vol. 66 (2002)
Osterloh, A., Amico, L., Falci, G., Fazio, R.: . Nature (London) 416, 608 (2002)
Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: . Phys. Rev. Lett. 90, 227902 (2003)
Wu, L.A., Sarandy, M.S., Lidar, D.A.: . Phys. Rev. Lett. 93, 250404 (2004)
Wu, L.A., Sarandy, M.S., Lidar, D.A., Sham, L.J.: . Phys. Rev. A 74, 052335 (2006)
Gu, S.J., Lin, H.Q., Li, Y.Q.: . Phys. Rev. A 68, 042330 (2003)
Gu, S.J., Tian, G.S., Lin, H.Q.: . Phys. Rev. A 71, 052322 (2005)
Hill, S., Wootters, W.K.: . Phys. Rev. Lett. 78, 5022 (1997)
Wootters, W.K.: . Rev, Phys. Lett. 80, 2245 (1998)
Alcaraz, F.C., Saguia, A., Sarandy, M.S.: . Phys. Rev. A 70, 032333 (2004)
Yang, M.F.: . Rev, Phys. A 71, 030302 (2005)
Kargarian, M., Jafari, R., Langari, A.: . Phys. Rev. A 76, 060304 (2007)
Kargarian, M., Jafari, R., Langari, A.: . Phys. Rev. A 77, 032346 (2008)
Hyllus, P., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., Smerzi, A.: . Phys. Rev. A 85, 022321 (2012)
Toth, G.: . Phys. Rev. A. 85, 022322 (2012)
Gessner, M., Pezzé, L., Smerzi, A.: . Phys. Rev. A 94, 020101 (2016)
Fisher, R.A.: Theory of statistical estimation. Proc. Cambridge Philod. Soc. 22, 700 (1925)
Cramer, H.: Mathematical methods of statistics (Princeton University Press NJ (1946)
Cover, T.M., Thomas, J.A.: Elements of information theory. Wiley, New York (2006)
Helstrom, C.W.: . Lett, Phys. A. 25, 101 (1976)
Helstrom, C.W.: Quantum detection and estimation theory. Academic Press, New York (1976)
Holevo, A.S.: Statistical structure of quantum theory. North-Holland, Amsterdam (1982)
Hübner, M.: . Phys. Lett. A 163, 239 (1992)
Hübner, M.: . Phys. Lett. A. 179, 226 (1993)
Braunstein, S.L., Caves, C.M.: . Phys. Rev. Lett. 72, 3439 (1994)
Braunstein, S.L., Caves, C.M., Milburn, G.J.: . Ann. Phys. 247, 135 (1996)
Boixo, S., Flammia, S.T., Caves, C.M., Geremia, J.M.: . Phys. Rev. Lett. 98, 090401 (2007)
Roy, S.M., Braunstein, S.L.: . Phys. Rev. Lett. 100, 220501 (2008)
Boixo, S., et al: . Phys. Rev. Lett. 101, 040403 (2008)
Jin, G.R., Kim, S.W.: . Phys. Rev. Lett. 99, 170405 (2007)
Pezzé, L., Smerzi, A.: . Phys. Rev Lett. 102, 100401 (2009)
Pezzé, L., Smerzi, A., Oberthaler, M.K., Schmied, R., Treutlein, P.: . Rev. Mod Phys. 90, 035005 (2018)
Sun, Z., Ma, J., Lu, X.M., Wang, X.G.: . Phys. Rev. A. 82, 022306 (2010)
Liu, C., Wang, D., Sun, W., Ye, L.: . Quan. Inf. Process. 16, 219 (2017)
Liu, X.M., Du, Z.Z., Cheng, W.W., Liu, J.M.: . Solid State Comm. 213, 24 (2015)
Liu, X.M., Cheng, W.W., Liu, J. -M.: . Sci. Rep. 6, 19359 (2016)
Hauke, P., Heyl, M., Tagliacozzo, L., Zoller, P.: . Nature Phys. 12, 778 (2016)
Frérot, I., Roscilde, T.: . Nat. Commun. 10, 577 (2019)
Gabbrielli, M., Smerzi, A., Pezzè, L.: . Sci. Rep. 8, 15663 (2018)
Gabrielli, M., Lepori, L., Pezzè, L.: . New J Phys. 21, 033039 (2019)
Ma, J., Wang X.: . Phys, Rev. A. 80, 012318 (2009)
Pezzé, L., Gabbrielli, M., Lepori, L., Smerzi, A.: . Phys. Rev. Lett. 119, 250401 (2017)
Zhang, Y.R., Zeng, Y., Fan, H., You, J.Q., Nori, F.: . Phys. Rev. Lett 120, 250501 (2018)
White, S.R.: . Phys. Rev. Lett. 69, 2863 (1992)
Foulkes, W.M., Mitas, L., Needs, R.J., Rajagopal, G.: . Rev. Mod. Phys. 73, 33 (2001)
Wilson, K.G.: . Rev. Mod. Phys. 47, 773 (1975)
Jafari, R., Langari, A., Akbari, A., Kim, K.S., Phys, J.: . J. Phys. Soc. Jpn 86, 024008 (2017)
Martin-Delgado, M.A.: Strongly correlated magnetic and superconducting systems, lecture notes in physics, Springer, 478 Springer (1997)
Martin-Delgado, M.A., Sierra, G.: . Int. J. Mod. Phys. A 11, 3145 (1996)
Jafari, R., Kargarian, M., Langari, A., Siahatgar, M.: . Phys. Rev. B 78, 214414 (2008)
Kargarian, M., Jafari, R., Langari, A.: . Phys. Rev. A 79, 042319 (2009)
Ma, F.W., Liu, S.X., Kong, X.M.: . Phys. Rev. A 83, 062309 (2011)
Ma, F.W., Liu, S.X., Kong, X.M.: . Phys. Rev. A 84, 042302 (2011)
Usman, M., Ilyas, A., Khan, K.: . Phys. Rev. A 92, 032327 (2015)
Usman, M., Ilyas, A., Khan, K.: . Quantum Inf Process 16, 232 (2017)
Usman, M., Khan, K.: . Euro. Phys. J. D 74, 181 (2020)
Wu, W., Xu, J.B.: . Europhys. Lett. 115, 40006 (2016)
Cheng, J.Q., Wu, W., Xu, J.B.: . Quant. Info. Process. 16, 231 (2017)
Khan, S., Khan, K.: . Eur. Phys. J. Plus 131, 208 (2016)
Khan, S., Khan, K.: . Physica B:, Condens. Matter 545, 289–296 (2018)
Joya, W., Khan, S., Khan, K., Alam, S.: . Eur. Phys. J. Plus 132, 215 (2017)
Joya, W., Khan, S., Khan, K.: . Physica B:, Condens. Matter 601, 412663 (2021)
Joya, W., Khan, K.: . Quantum Inf Processing 16(10), 243 (2017)
Joya, W.: . Int. J. Quantum Inf. 13(5), 1550035 (2015)
Joya, W.: . Pramana J Phys 93, 94 (2019)
Efrati, E., Wang, Z., Kolan, A., Kadanoff, L.P.: . Rev. Mod. Phys 86, 647 (2013)
Sarıyer, O.S., Berker, A.N., Hinczewski, M.: . Phys. Rev. B 77, 134413 (2008)
Sarıyer, O.S.: . Philos. Mag. 99, 1787–1824 (2019)
Sarıyer, O. S.: . Turk. J. Phys. 44, 288–301 (2020)
Suzuki, M., Takano, H.: . Phys. Lett. 69, 426–428 (1979)
Takano, H., Suzuki, M.: . J. Stat. Phys. 26, 635–663 (1981)
Dzyaloshinsky, I.: . J. Phys. Chem. Solids 4, 241 (1958)
Moriya, T.: . Phys. Rev. 120, 91 (1960)
Kohgi, M., Iwasa, K., Mignot, J.M., Fŭak, B., Gegenwart, P., Lang, M., et al: . Phys. Rev. Lett. 86, 2439 (2001)
Tsukada, I., Takeya, J., Masuda, T., Uchinokura, K.: . Phys. Rev. Lett. 87, 127203 (2001)
Loss, D., DiVincenzo, D.P.: . Phys. Rev. A 57, 120 (1998)
Raussendorf, R., Briegel, H.J.: . Phys. Rev. Lett. 86, 5188 (2001)
Langari, A., et al: . J. Phys.: Condens. Matter 25, 406002 (2013)
Jafari, R., et al: . J. Phys.: Condens. Matter 31, 495601 (2019)
Sachs, B., et al: . Phys. Rev. B 88(R), 201402 (2013)
Lee, J.U., et al: . Nano. Lett. 16, 7433 (2016)
Barnes, T.: . Int. J. Mod. Phys. C 2, 659 (1991)
Makivić, M.S., Ding, H.Q.: . Phys. Rev. B 43, 3562 (1991)
McGuire, M.A., et al: . Chem. Matter. 27, 612 (2015)
Lee, K.W., Lee, C.E., Kim, I. -m.: . Solid State Commun. 135, 95 (2005)
deSousaa, J.R., Brancob, N.S., Boechatc, B., Cordeiroc, C.: . Physica A 328, 167 (2003)
Lima, L.S.: . Eur. Phys. J. D 73, 6 (2019)
Iftikhar, M.T., Usman, M., Khan, K.: . Eur. Phys. J. Plus 136, 491 (2021)
Iftikhar, M.T., Usman, M., Khan, K.: . Quantum Inf Processing 20, 259 (2021)
Zeng, C., Farell, D.J.J., Bishop, R.F.: . J. Stat. Phys. 90, 327 (1998)
Nishimori, H., Ozeki, Y.: . J. Phys. Soc. Jpn. 58, 1027 (1989)
Li, N., Luo, S.L.: . Phys. Rev. A 88, 014301 (2013)
Luo, S.L.: . Theor. Math. Phys. 143, 681 (2005)
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Khalid Khan proposed the idea. M.T. Iftikhar and M. Usman carried out the calculations and plotted the figures. M.T. Iftikhar wrote the paper under the guidance of M. Usman and Khalid Khan. All authors discussed the results and commented on the manuscript.
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Iftikhar, M.T., Usman, M. & Khan, K. Effect of Dzyaloshinskii-Moriya Interaction on the Entanglement and Quantum Phase Transition in Two-Dimensional XXZ Model. Int J Theor Phys 61, 20 (2022). https://doi.org/10.1007/s10773-022-05021-0
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DOI: https://doi.org/10.1007/s10773-022-05021-0