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Quantum Information Processing
Erschienen in: Quantum Information Processing 9/2020

01.08.2020

On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions

verfasst von: M. A. Yurischev

Erschienen in: Quantum Information Processing | Ausgabe 9/2020

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Abstract

The anisotropic Heisenberg two-spin-1/2 model in an inhomogeneous magnetic field with both antisymmetric Dzyaloshinsky–Moriya and symmetric Kaplan–Shekhtman–Entin-Wohlman–Aharony cross interactions is considered at thermal equilibrium. Using a group-theoretical approach, we find fifteen spin Hamiltonians and as many corresponding Gibbs density matrices (quantum states) whose eigenvalues are expressed only through square radicals. We also found local unitary transformations that connect nine of this fifteen state collection, and one of them is the X quantum state. Since such quantum correlations as quantum entanglement, quantum discord, one-way quantum work deficit, and others are known for the X state, this allows to get the quantum correlations for any member from the nine state family. Further, we show that the remaining six quantum states are separable and that they are also connected by local unitary transformations, but, however, now the case with known correlations beyond entanglement is generally not available.
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Fußnoten
1
One may also choose \({\tilde{Y}}=\frac{1}{\sqrt{2}} \left( \begin{array}{ll} 1&{}i\\ i&{}1 \end{array} \right) \) that leads to the relations \({\tilde{Y}}^\dagger \sigma _x {\tilde{Y}}=\sigma _x\), \({\tilde{Y}}^\dagger \sigma _y {\tilde{Y}}=\sigma _z\), and \({\tilde{Y}}^\dagger \sigma _z {\tilde{Y}}=-\sigma _y\).
 
2
We omit the case \(U_{00} (=E)\) because \(\{E\}\) is the trivial group.
 
Literatur
1.
Dzialoshinskii, I.E.: Thermodynamic theory of “weak” ferromagnetism in antiferromagnetic substances. ZhETF 32, 1547 (1957) [in Russian]; Sov. Phys. JETP 5, 1259 (1957) [in English]
2.
Dzyaloshinsky, I.: A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241 (1958)ADS
3.
Dzialoshinskii, I.E.: The magnetic structure of fluorides of the transition metals. ZhETF 33, 1454 (1957) [in Russian]; Sov. Phys. JETP 6, 1120 (1958) [in English]
4.
Moriya, T.: New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228 (1960)ADS
5.
Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960)ADS
6.
Kaplan, T.A.: Single-band Habbard model with spin-orbit coupling. Z. Phys. B Condens. Matter 49, 313 (1983)ADS
7.
Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism. Phys. Rev. Lett. 69, 836 (1992)ADS
8.
Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Bond-dependent symmetric and antisymmetric superexchange interactions in \({\rm La_2CuO_4}\). Phys. Rev. B 47, 174 (1993)ADS
9.
Zheludev, A., Maslov, S., Tsukada, I., Zaliznyak, I., Regnault, L.P., Masuda, T., Uchinokura, K., Erwin, R., Shirane, G.: Experimental evidence for Shekhtman–Entin-Wohlman–Aharony interactions in \({\rm Ba_2CuGe_2O_7}\) (1998). arXiv:​cond-mat/​9805236v1
10.
Zheludev, A., Maslov, S., Tsukada, I., Zaliznyak, I., Regnault, L.P., Masuda, T., Uchinokura, K., Erwin, R., Shirane, G.: Experimental evidence for Kaplan-Shekhtman–Entin-Wohlman–Aharony interactions in \({\rm Ba_2CuGe_2O_7}\). Phys. Rev. Lett. 81, 5410 (1998)ADS
11.
Yildirim, T., Harris, A.B., Aharony, A., Entin-Wohlman, O.: Anisotropic spin Hamiltonians due to spin-orbit and Coulomb exchange interactions. Phys. Rev. B 52, 10239 (1995)ADS
12.
Zhang, G.-F.: Thermal entanglement and teleportation in two-qubit Heisenberg chain with Dzyaloshinski–Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75, 034304 (2007)ADS
13.
Li, D.-C., Wang, X.-P., Cao, Z.-L.: Thermal entanglement in the anisotropic Heisenberg XXZ model with Dzyaloshinskii–Moriya interaction. J. Phys. Condens. Matter 20, 325229 (2008)
14.
Kargarian, M., Jafari, R., Langari, A.: Dzyaloshinskii–Moriya interaction and anisotropy effects on the entanglement of Heisenberg model. Phys. Rev. A 79, 042319 (2009)ADS
15.
Li, D.-C., Cao, Zh-L: Effect of different Dzyaloshinskii–Moriya interactions on entanglement in the Heisenberg XYZ chain. Int. J. Quantum Inf. 7, 547 (2009)MATH
16.
Chen, Y.-X., Yin, Z.: Thermal quantum discord in anisotropic Heisenberg XXZ model with Dzyaloshinskii–Moriya interaction. Commun. Theor. Phys. (China) 54, 60 (2010)ADSMATH
17.
Tursun, M., Abliz, A., Mamtimin, R., Abliz, A., Pan-Pan, Q.: Various correlations in anisotropic Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction. Chin. Phys. Lett. 30, 030303 (2013)ADS
18.
Zidan, N.: Quantum discord of a two-qubit anisotropy XXZ Heisenberg chain with Dzyaloshinskii–Moriya interaction. J. Quantum Inf. Sci. 4, 104 (2014)
19.
Park, D.: Thermal entanglement and thermal discord in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions. Quantum Inf. Process. 18, 172 (2019)ADSMathSciNet
20.
Sun, Y., Ma, X.-P., Guo, J.-L.: Dynamics of non-equilibrium thermal quantum correlation in a two-qubit Heisenberg XYZ model. Quantum Inf. Process. 19, 98 (2020)ADSMathSciNet
21.
Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008)ADSMathSciNetMATH
22.
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetMATH
23.
Céleri, L.C., Maziero, J., Serra, R.M.: Theoretical and experimental aspects of quantum discord and related measures. Int. J. Quantum Inf. 11, 1837 (2011)MathSciNetMATH
24.
Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)ADS
25.
Aldoshin, S.M., Fel’dman, E.B., Yurishchev, M.A.: Quantum entanglement and quantum discord in magnetoactive materials (Review Article). Fiz. Nizk. Temp. 40, 5 (2014) [in Russian]; Low Temp. Phys. 40, 3 (2014) [in English]
26.
Adesso, G., Bromley, T.R., Cianciaruso, M.: Measures and applications of quantum correlations. J. Phys. A Math. Theor. 49, 473001 (2016)ADSMathSciNetMATH
27.
Fanchini, F.F., Soares-Pinto, D.O., Adesso, G. (eds.): Lectures on General Quantum Correlations and Their Applications. Springer, Berlin (2017)MATH
28.
Bera, A., Das, T., Sadhukhan, D., Roy, S.S., De Sen, A., Sen, U.: Quantum discord and its allies: a review of recent progress. Rep. Prog. Phys. 81, 024001 (2018)ADSMathSciNet
29.
Brodutch, A., Modi, K.: Criteria for measures of quantum correlations. Quantum Inf. Comput. 12, 0721 (2012)MathSciNetMATH
30.
Yu, T., Eberly, J.H.: Evolution from entanglement to decoherence of bipartite mixed “X” states. Quantum Inf. Comput. 7, 459 (2007)MathSciNetMATH
31.
Rau, A.R.P.: Algebraic characterization of \(X\)-states in quantum information. J. Phys. A: Math. Theor. 42, 412002 (2009)MathSciNetMATH
32.
Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley, Reading (1964)MATH
33.
Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit \(X\) states. Phys. Rev. A 84, 042313 (2011)ADS
34.
Huang, Y.: Quantum discord for two-qubit \(X\) states: analytical formula with very small worst-case error. Phys. Rev. A 88, 014302 (2013)ADS
35.
Jing, N., Yu, B.: Quantum discord of \(X\)-states as optimization of a one variable function. J. Phys. A Math. Theor. 49, 385302 (2016)ADSMathSciNetMATH
36.
37.
Yurishchev, M.A.: NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore. ZhETF 146, 946 (2014) [in Russian]; J. Exp. Theor. Phys. 119, 828 (2014) [in English]. arXiv:​1503.​03316v1 [quant-ph]
38.
39.
Yurischev, M.A.: Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states. Quantum Inf. Process. 16, 249 (2017)ADSMathSciNetMATH
40.
Wang, Y.-K., Jing, N., Fei, S.-M., Wang, Z.-X., Cao, J.-P., Fan, H.: One-way deficit of two-qubit \(X\) states. Quantum Inf. Process. 14, 2487 (2015)ADSMATH
41.
Ye, B.-L., Fei, S.-M.: A note on one-way quantum deficit and quantum discord. Quantum Inf. Process. 15, 279 (2016)ADSMathSciNetMATH
42.
Ye, B.-L., Wang, Y.-K., Fei, S.-M.: One-way quantum deficit and decoherence for two-qubit \(X\) states. Int. J. Theor. Phys. 55, 2237 (2016)MATH
43.
Yurischev, M.A.: Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states. Quantum Inf. Process. 17, 6 (2018)ADSMathSciNetMATH
44.
Yurischev, M.A.: Phase diagram for the one-way quantum deficit of two-qubit X states. Quantum Inf. Process. 18, 124 (2019)ADSMathSciNetMATH
45.
Yurischev, M.A.: Temperature-field phase diagram of one-way quantum deficit in two-qubit XXZ spin systems. Quantum Inf. Process. 19, 110 (2020)ADSMathSciNet
46.
Weaver, J.R.: Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors. Am. Math. Mon. 92, 711 (1985)MathSciNetMATH
47.
48.
Yurishchev, M.A.: On the theory of double Ising chains. The model in zero external field. Fiz. Nizk. Temp. 4, 646 (1978) [in Russian]; Sov. J. Low Temp. Phys. 4, 311 (1978) [in English]
49.
Hamermesh, M.: Group Theory and Its Application to Physical Problems. Addison-Wesley, Massachusetts (1962)MATH
50.
Bethe, H.A.: Intermediate Quantum Mechanics. Benjamin, New York (1964)
51.
Fel’dman, E.B., Kuznetsova, E.I., Yurishchev, M.A.: Quantum correlations in a system of nuclear \(s=1/2\) spins in a strong magnetic field. J. Phys. A Math. Theor. 45, 475304 (2012)ADSMathSciNetMATH
52.
Rau, A.R.P.: Manipulating two-spin coherences and qubit pairs. Phys. Rev. A 61, 032301 (2000)ADSMathSciNet
53.
Zhang, J., Vala, J., Sastry, S., Whaley, K.B.: Geometric theory of nonlocal two-qubit operations. Phys. Rev. A 67, 042313 (2003)ADSMathSciNet
54.
Marceaux, J.P., Rau, A.R.P.: Placing Kirkman’s schoolgirls and quantum spin pairs on the Fano plane: a rainbow of four primary colors, a harmony of fifteen tones. arXiv:​1905.​06914v1 [quant-ph]
55.
Marceaux, J.P., Rau, A.R.P.: Mapping qubit algebras to combinatorial designs. Quantum Inf. Process. 19, 49 (2020)ADSMathSciNet
56.
57.
Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)ADSMathSciNetMATH
58.
Dakić, B., Vedral, V., Brukner, Č.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSMATH
59.
Zhou, J., Hu, X., Jing, N.: Quantum discord of certain two-qubit states. Int. J. Theor. Phys. 59, 415 (2020)MathSciNetMATH
Metadaten
Titel
On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions
verfasst von
M. A. Yurischev
Publikationsdatum
01.08.2020
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 9/2020
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02835-x

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