Thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain with impurities

doi:10.1088/1674-1056/abbbde

中国物理B ›› 2020, Vol. 29 ›› Issue (11): 110308-.doi: 10.1088/1674-1056/abbbde

Meng-Ru Ma(马梦如)¹, Yi-Dan Zheng(郑一丹)¹, Zhu Mao(毛竹)¹^,†(), Bin Zhou(周斌)¹^,^‡()

收稿日期:2020-08-13 修回日期:2020-09-01 接受日期:1900-01-01 出版日期:2020-11-05 发布日期:2020-11-03

Thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain with impurities

Meng-Ru Ma(马梦如), Yi-Dan Zheng(郑一丹), Zhu Mao(毛竹)^†, and Bin Zhou(周斌)^‡

Department of Physics, Hubei University, Wuhan 430062, China

Received:2020-08-13 Revised:2020-09-01 Accepted:1900-01-01 Online:2020-11-05 Published:2020-11-03
Contact: ^†Corresponding author. E-mail: maozhu@hubu.edu.cn ^‡Corresponding author. E-mail: binzhou@hubu.edu.cn
Supported by:
the National Natural Science Foundation of China (Grant No. 12074101), the Science Fund for the New Century Excellent Talents in University of the Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

摘要/Abstract

Abstract:

We investigate the effect of impurities on the thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain, where four interstitial Heisenberg spins are localized on the vertices of a rectangular plaquette in a unit block. By using the transfer-matrix approach, we numerically calculate the partition function and the reduced density matrix of this model. The bipartite thermal entanglement between different Heisenberg spin pairs is quantified by the concurrence. We also discuss the fluctuations caused by the impurities through the uniform distribution and the Gaussian distribution. Considering the effects of the external magnetic field, temperature, Heisenberg and Ising interactions as well as the parameter of anisotropy on the thermal entanglement, our results show that comparing with the case of the clean model, in both the two-impurity model and the impurity fluctuation model the entanglement is more robust within a certain range of anisotropic parameters and the region of the magnetic field where the entanglement occurred is also larger.

Key words: thermal entanglement, Ising-Heisenberg butterfly-shaped chain, impurities, transfer-matrix approach

Meng-Ru Ma(马梦如), Yi-Dan Zheng(郑一丹), Zhu Mao(毛竹), Bin Zhou(周斌). [J]. 中国物理B, 2020, 29(11): 110308-.

Meng-Ru Ma(马梦如), Yi-Dan Zheng(郑一丹), Zhu Mao(毛竹), and Bin Zhou(周斌). Thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain with impurities[J]. Chin. Phys. B, 2020, 29(11): 110308-.

[1]	Bell J S 1987 Speakable and unspeakable in quantum mechanics Cambridge Cambridge University
[2]	Peres A 2006 Quantum theory: concepts and methods Springer Science & Business Media
[3]	Bennett C H Brassard G Crépeau C Jozsa R Peres A Wootters W K 1993 Phys. Rev. Lett. 70 1895 DOI: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895
[4]	Boschi D Branca S de Martini F Hardy L Popescu S 1998 Phys. Rev. Lett. 80 1121 DOI: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.80.1121
[5]	Venuti L C Giampaolo S Illuminati F Zanardi P 2007 Phys. Rev. A 76 052328 DOI: 10.1103/PhysRevA.76.052328
[6]	Bennett C H 1992 Phys. Rev. Lett. 68 3121 DOI: 10.1103/PhysRevLett.68.3121
[7]	Shor P W Preskill J 2000 Phys. Rev. Lett. 85 441 DOI: 10.1103/PhysRevLett.85.441
[8]	Lo H K Ma X Chen K 2005 Phys. Rev. Lett. 94 230504 DOI: 10.1103/PhysRevLett.94.230504
[9]	Gisin N Massar S 1997 Phys. Rev. Lett. 79 2153 DOI: 10.1103/PhysRevLett.79.2153
[10]	Scarani V Iblisdir S Gisin N Acin A 2005 Rev. Mod. Phys. 77 1225 DOI: 10.1103/RevModPhys.77.1225
[11]	Wang M H Cai Q Y 2019 Phys. Rev. A 99 012324 DOI: 10.1103/PhysRevA.99.012324
[12]	Wang X 2002 Phys. Rev. A 66 034302 DOI: 10.1103/PhysRevA.66.034302
[13]	Zhou L Song H S Guo Y Q Li C 2003 Phys. Rev. A 68 024301 DOI: 10.1103/PhysRevA.68.024301
[14]	Zhang G F Li S S 2005 Phys. Rev. A 72 034302 DOI: 10.1103/PhysRevA.72.034302
[15]	Vedral V Plenio M B Rippin M A Knight P L 1997 Phys. Rev. Lett. 78 2275 DOI: 10.1103/PhysRevLett.78.2275
[16]	Hill S Wootters W K 1997 Phys. Rev. Lett. 78 5022 DOI: 10.1103/PhysRevLett.78.5022
[17]	Plenio M B Vedral V 1998 Contemp. Phys. 39 431 DOI: 10.1080/001075198181766
[18]	Wootters W K 1998 Phys. Rev. Lett. 80 2245 DOI: 10.1103/PhysRevLett.80.2245
[19]	Coffman V Kundu J Wootters W K 1999 Phys. Rev. A 61 052306 DOI: 10.1103/physreva.61.052306
[20]	Gunlycke D Kendon V Vedral V Bose S 2001 Phys. Rev. A 64 042302 DOI: 10.1103/PhysRevA.64.042302
[21]	Wang X 2001 Phys. Rev. A 64 012313 DOI: 10.1103/PhysRevA.64.012313
[22]	Kargarian M Jafari R Langari A 2008 Phys. Rev. A 77 032346 DOI: 10.1103/PhysRevA.77.032346
[23]	Amico L Fazio R Osterloh A Vedral V 2008 Rev. Mod. Phys. 80 517 DOI: 10.1103/RevModPhys.80.517
[24]	Bethe H 1931 Z. Phys. 71 205 DOI: 10.1007/BF01341708
[25]	Baxter R J 1982 Exactly solved models in statistical mechanics New York Academic Press
[26]	Yeomans J M 1992 Statistical mechanics of phase transitions Clarendon Press
[27]	Rommer S Eggert S 1999 Phys. Rev. B 59 6301 DOI: 10.1103/PhysRevB.59.6301
[28]	Osenda O Huang Z Kais S 2003 Phys. Rev. A 67 062321 DOI: 10.1103/PhysRevA.67.062321
[29]	Santos L F 2003 Phys. Rev. A 67 062306 DOI: 10.1103/PhysRevA.67.062306
[30]	Apollaro T J Plastina F 2006 Phys. Rev. A 74 062316 DOI: 10.1103/PhysRevA.74.062316
[31]	Huang Z Osenda O Kais S 2004 Phys. Lett. A 322 137 DOI: 10.1016/j.physleta.2004.01.022
[32]	Cai J M Zhou Z W Guo G C 2006 Phys. Lett. A 352 196 DOI: 10.1016/j.physleta.2005.11.072
[33]	Hoyos J A Rigolin G 2006 Phys. Rev. A 74 062324 DOI: 10.1103/PhysRevA.74.062324
[34]	Rule K C Reehuis M Gibson M C R Ouladdiaf B Gutmann M J Hoffmann J U Gerischer S Tennant D A Süllow S Lang M 2011 Phys. Rev. B 83 104401 DOI: 10.1103/PhysRevB.83.104401
[35]	Jeschke H Opahle I Kandpal H Valentí R Das H Saha-Dasgupta T Janson O Rosner H Brühl A Wolf B Lang M Richter J Hu S Wang X Peters R Pruschke T Honecker A 2011 Phys. Rev. Lett. 106 217201 DOI: 10.1103/PhysRevLett.106.217201
[36]	Qiao J Zhou B 2015 Chin. Phys. B 24 110306 DOI: 10.1088/1674-1056/24/11/110306
[37]	Zheng Y D Mao Z Zhou B 2017 Chin. Phys. B 26 070302 DOI: 10.1088/1674-1056/26/7/070302
[38]	Rojas O Rojas M Ananikian N S de Souza S M 2012 Phys. Rev. A 86 042330 DOI: 10.1103/PhysRevA.86.042330
[39]	Rojas O Rojas M de Souza S M Torrico J Strečka J Lyra M L 2017 Physica A 486 367 DOI: 10.1016/j.physa.2017.05.099
[40]	Verkholyak T Strečka J 2013 Phys. Rev. B 88 134419 DOI: 10.1103/PhysRevB.88.134419
[41]	Rojas O Strečka J Lyra M L 2013 Phys. Lett. A 377 920 DOI: 10.1016/j.physleta.2013.02.013
[42]	Strečka J Rojas O Verkholyak T Lyra M L 2014 Phys. Rev. E 89 022143 DOI: 10.1103/PhysRevE.89.022143
[43]	Karl’ová K Strečka J Lyra M L 2018 Phys. Rev. B 97 104407 DOI: 10.1103/PhysRevB.97.104407
[44]	Carvalho I M Rojas O de Souza S M Rojas M 2019 Quantum Inf. Process. 18 134 DOI: 10.1007/s11128-019-2253-2
[45]	Freitas M Filgueiras C Rojas M 2019 Ann. Phys. 531 1900261 DOI: 10.1002/andp.201900261
[46]	Zad H A Ananikian N Kenna R 2019 J. Phys.: Condens. Matter 31 445802 DOI: 10.1088/1361-648x/ab3136
[47]	Zheng Y D Mao Z Zhou B 2019 Chin. Phys. B 28 120307 DOI: 10.1088/1674-1056/ab53cc

Thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain with impurities

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