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Quantum Information Processing
Published in: Quantum Information Processing 9/2017

01-09-2017

Multipartite entanglement in an XXZ spin chain with Dzyaloshinskii–Moriya interaction and quantum phase transition

Authors: Jun-Qing Cheng, Wei Wu, Jing-Bo Xu

Published in: Quantum Information Processing | Issue 9/2017

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Abstract

We investigate the multipartite entanglement and trace distance of the one-dimensional anisotropic spin-1/2 XXZ spin chain with the Dzyaloshinskii–Moriya interaction and find that the Dzyaloshinskii–Moriya interaction can influence the entanglement distribution and increase the proportion of multipartite entanglement in the entanglement structure. Furthermore, we explore the quantum phase transition of the XXZ spin chain with Dzyaloshinskii–Moriya interaction by making use of the multipartite entanglement and trace distance along with the quantum renormalization group method. It is found that the first derivatives of renormalized multipartite entanglement and trace distance for the ground state have dramatic changes near the critical point, and the renormalized multipartite entanglement and trace distance obey the universal finite-size scaling laws in the vicinity of the quantum critical point.
previous article Spatial dependence of entanglement renormalization in XY model
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Literature
1.
Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transition. Nature 416(6881), 608–610 (2002)ADSCrossRef
2.
Wu, L.A., Sarandy, M.S., Lidar, D.A.: Quantum phase transitions and bipartite entanglement. Phys. Rev. Lett. 93, 250–404 (2004)MathSciNetCrossRef
3.
4.
5.
6.
Jafari, R., Langari, A.: Phase diagram of the one-dimensional \({S}=1/2\) XXZ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Phys. Rev. B 76(1), 014412 (2007)ADSCrossRef
7.
Kargarian, M., Jafari, R., Langari, A.: Dzyaloshinskii–moriya interaction and anisotropy effects on the entanglement of the Heisenberg model. Phys. Rev. A 79, 042319 (2009)ADSCrossRef
8.
Yao, Y., Li, H.W., Zhang, C.M., Yin, Z.Q., Chen, W., Guo, G.C., Han, Z.F.: Performance of various correlation measures in quantum phase transitions using the quantum renormalization-group method. Phys. Rev. A 86(4), 042102 (2012)ADSCrossRef
9.
Efrati, E., Wang, Z., Kolan, A., Kadanoff, L.P.: Real-space renormalization in statistical mechanics. Rev. Mod. Phys 86(2), 647–667 (2013)ADSCrossRef
10.
Usman, M., Ilyas, A., Khan, K.: Quantum renormalization group of the XY model in two dimensions. Phys. Rev. A 92(3), 032327 (2015)ADSCrossRef
11.
Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53(4), 2046 (1996)ADSCrossRef
12.
Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)ADSCrossRef
13.
Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54(5), 3824 (1996)ADSMathSciNetCrossRef
14.
Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997)ADSCrossRef
15.
16.
Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000)ADSCrossRef
17.
Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96(22), 220503 (2006)ADSCrossRef
18.
19.
de Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89, 034303 (2014)ADSCrossRef
20.
Bai, Y.K., Xu, Y.F., Wang, Z.: General monogamy relation for the entanglement of formation in multiqubit systems. Phys. Rev. Lett. 113(10), 100503 (2014)ADSCrossRef
21.
Gilchrist, A., Langford, N.K., Nielsen, M.A.: Distance measures to compare real and ideal quantum processes. Phys. Rev. A 71(6), 062310 (2005)ADSCrossRef
22.
Luo, D.W., Xu, J.B.: Trace distance and scaling behavior of a coupled cavity lattice at finite temperature. Phys. Rev. A 87(1), 013801 (2013)ADSCrossRef
23.
Luo, D.W., Xu, J.B.: Quantum phase transition by employing trace distance along with the density matrix renormalization group. Ann. Phys. 354, 298–305 (2015)ADSMathSciNetCrossRef
24.
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge university press, Cambridge (2010)CrossRefMATH
25.
Foulkes, W.M., Mitas, L., Needs, R.J., Rajagopal, G.: Quantum monte carlo simulations of solids. Rev. Mod. Phys. 73, 33–83 (2001)ADSCrossRef
26.
White, S.R.: Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69(19), 2863–2866 (1992)ADSCrossRef
27.
Toskovic, R., Van Berg, R., Spinelli, A., Eliens, I.S., Den Toorn, B.V., Bryant, B., Caux, J.S., Otte, A.F.: Atomic spin-chain realization of a model for quantum criticality. Nat. Phys. 12(7), 656–660 (2016)
28.
Breunig, O., Garst, M., Sela, E., Buldmann, B., Becker, P., Bohatý, L., Müller, R., Lorenz, T.: Spin-\(\frac{1}{2}\) \(XXZ\) chain system \(Cs_{2}CoCl_{4}\) in a transverse magnetic field. Phys. Rev. Lett. 111, 187202 (2013)ADSCrossRef
29.
Dzyaloshinsky, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4(4), 241–255 (1958)ADSCrossRef
30.
Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120(1), 91 (1960)ADSCrossRef
31.
Kohgi, M., Iwasa, K., Mignot, J.M., Fåk, B., Gegenwart, P., Lang, M., et al.: Staggered field effect on the one-dimensional \(S = 1 / 2\) antiferromagnet \(Yb_{4}As{3}\). Phys. Rev. Lett. 86, 2439–2442 (2001)ADSCrossRef
32.
Tsukada, I., Takeya, J., Masuda, T., Uchinokura, K.: Two-stage spin-flop transitions in the \(S = 1 / 2\), antiferromagnetic spin chain \(Ba_Cu_{2}Si_{2}O_{7}\). Phys. Rev. Lett. 87, 127203 (2001)ADSCrossRef
33.
Peres, A., Mayer, M.E.: Quantum theory: concepts and methods. Phys. Today 47(12), 65–66 (1994)ADSCrossRef
34.
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)ADSCrossRefMATH
35.
36.
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefMATH
37.
Jafari, R., Langari, A.: Three-qubits ground state and thermal rntanglement of anisotropic Heisenberg (XXZ) and ising models with dzyaloshinskii–moriya interaction. Int. J. Quantum Inf. 09(4), 1057–1079 (2011)CrossRef
38.
Martin-Delgado, M.A., Sierra, G.: Analytic formulations of the density matrix renormalization group. Int. J. Mod. Phys. A 11(17), 3145–3174 (1996)ADSCrossRef
39.
Kargarian, M., Jafari, R., Langari, A.: Renormalization of concurrence: the application of the quantum renormalization group to quantum-information systems. Phys. Rev. A 76, 060304 (2007)ADSCrossRef
40.
Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66(3), 355–358 (2002)MathSciNetCrossRef
41.
Yang, M.F.: Reexamination of entanglement and the quantum phase transition. Phys. Rev. A 71(3), 309–315 (2005)
42.
Qian, X., Shi, T., Li, Y., Song, Z., Sun, C.: Characterizing entanglement by momentum jump in the frustrated Heisenberg ring at a quantum phase transition. Phys. Rev. A 72(1), 012333 (2005)ADSCrossRef
43.
Montakhab, A., Asadian, A.: Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model. Phys. Rev. A 82(6), 062313 (2010)ADSCrossRef
44.
Hofmann, M., Osterloh, A., Gühne, O.: Scaling of genuine multiparticle entanglement close to a quantum phase transition. Phys. Rev. B 89, 134101 (2014)ADSCrossRef
45.
Wu, W., Xu, J.B.: Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems. Europhys. Lett. 115(4), 40006 (2016)ADSCrossRef
46.
Giampaolo, S.M., Hiesmayr, B.C.: Genuine multipartite entanglement in the XY model. Phys. Rev. A 88, 052305 (2013)ADSCrossRef
47.
Metadata
Title
Multipartite entanglement in an XXZ spin chain with Dzyaloshinskii–Moriya interaction and quantum phase transition
Authors
Jun-Qing Cheng
Wei Wu
Jing-Bo Xu
Publication date
01-09-2017
Publisher
Springer US
Published in
Quantum Information Processing / Issue 9/2017
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-017-1683-y

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