Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Quantum Information Processing
Published in: Quantum Information Processing 2/2017

01-02-2017

Quantum phase transition in the Dzyaloshinskii–Moriya interaction with inhomogeneous magnetic field: Geometric approach

Authors: G. Najarbashi, B. Seifi

Published in: Quantum Information Processing | Issue 2/2017

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we generalize the results of Oh (Phys Lett A 373:644–647, 2009) to Dzyaloshinskii–Moriya model under non-uniform external magnetic field to investigate the relation between entanglement, geometric phase (or Berry phase) and quantum phase transition. We use quaternionic representation to relate the geometric phase to the quantum phase transition. For small values of DM parameter, the Berry phase is more appropriate than the concurrence measure, while for large values, the concurrence is a good indicator to show the phase transition. On the other hand, by increasing the DM interaction the phase transition occurs for large values of anisotropy parameter. In addition, for small values of magnetic field the concurrence measure is appropriate indicator for quantum phase transition, but for large values of magnetic field the Berry phase shows a sharp changes in the phase transition points. The results show that the Berry phase and concurrence form a complementary system from phase transition point of view.
previous article Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Sachdev, S.: Quantum Phase Transitions, 2nd edn. Cambridge University Press, Cambridge (2011)CrossRefMATH
2.
Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. University of Illinois, Urbana-Champaign (1992)MATH
3.
4.
5.
6.
7.
Shapere, A., Wilczek, F.: Geometric Phases in Physics. World Scientific, Singapore (1989)MATH
8.
Najarbashi, G., Ahadpour, S., Fasihi, M.A., Tavakoli, Y.: Geometry of a two-qubit state and intertwining quaternionic conformal mapping under local unitary transformations. J. Phys. A Math. Theor. 40, 6481–6489 (2007)ADSMathSciNetCrossRefMATH
9.
Najarbashi, G., Seifi, B., Mirzaei, S.: Two- and three-qubit geometry, quaternionic and octonionic conformal maps, and intertwining stereographic projection. Quantum Inf. Process. 15, 509528 (2016)MathSciNetCrossRefMATH
10.
11.
12.
Oh, S., Huang, Z., Peskin, U., Kais, S.: Entanglement, Berry phases, and level crossings for the atomic Breit–Rabi Hamiltonian. Phys. Rev. A 78, 062106 (2008)ADSMathSciNetCrossRef
13.
Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)ADSMathSciNetCrossRefMATH
14.
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetCrossRefMATH
15.
16.
Murao, M., Jonathan, D., Plenio, M.B., Vedral, V.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A. 59, 156 (1999)ADSCrossRef
17.
Schrödinger, E.: Probability relations between separated systems. Proc. Camb. Phil. Soc. 31, 555 (1935)ADSCrossRefMATH
18.
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRefMATH
19.
Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)
20.
Maleki, Y., Khashami, F., Mousavi, Y.: Entanglement of three-spin states in the context of SU(2) coherent states. Int. J. Theor. Phys. 54, 210 (2015)CrossRefMATH
21.
Angelakis, D.G., Christandl, M., Ekert, A., Kay, A., Kulik, S.: Quantum Information Processing: From Theory to Experiment, vol. 199. Computer and Systems Sciences, vol. 199. IOS Press, NATO Science Series, Amsterdam (2006)MATH
22.
Gunlycke, D., Kendon, V.M., Vedral, V., Bose, S.: Thermal concurrence mixing in a one-dimensional Ising model. Phys. Rev. A 64, 042302 (2001)ADSCrossRef
23.
Yang, Z., Yang, L., Dai, J., Xiang, T.: Rigorous solution of the spin-1 quantum ising model with single-ion anisotropy. Phys. Rev. Lett. 100, 067203 (2008)ADSCrossRef
24.
Kamta, G.L., Starace, A.F.: Anisotropy and magnetic field effects on the entanglement of a two qubit Heisenberg XY chain. Phys. Rev. Lett. 88, 107901 (2002)ADSCrossRef
25.
Wang, X.: Thermal and ground-state entanglement in Heisenberg XX qubit rings. Phys. Rev. A 66, 034302 (2002)ADSCrossRef
26.
Sun, Y., Chen, Y., Chen, H.: Thermal entanglement in the two-qubit Heisenberg XY model under a nonuniform external magnetic field. Phys. Rev. A 68, 044301 (2003)ADSCrossRef
27.
Kao, Z.C., Ng, J., Yeo, Y.: Three-qubit thermal entanglement via entanglement swapping on two-qubit Heisenberg XY chains. Phys. Rev. A 72, 062302 (2005)ADSCrossRef
28.
Zhu, S.L.: Scaling of geometric phases close to the quantum phase transition in the XY spin chain. Phys. Rev. Lett. 96, 077206 (2006)ADSCrossRef
29.
Asoudeh, M., Karimipour, V.: Thermal entanglement of spins in an inhomogeneous magnetic field. Phys. Rev. A 71, 022308 (2005)ADSCrossRef
30.
Zhang, G.F.: Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski–Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75, 034304 (2007)ADSCrossRef
31.
Zhang, G.F., Li, S.S.: Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field. Phys. Rev. A 72, 034302 (2005)ADSCrossRef
32.
Kargarian, M., Jafari, R., Langari, A.: Renormalization of entanglement in the anisotropic Heisenberg (XXZ) model. Phys. Rev. A 77, 032346 (2008)ADSCrossRef
33.
Dzyaloshinsky, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241 (1958)ADSCrossRef
34.
Moriya, T.: New mechanism of anisotropic super exchange interaction. Phys. Rev. Lett. 4, 228 (1960)ADSCrossRef
35.
Kheirandish, F., Akhtarshenas, S.J., Mohammadi, H.: Effect of spin–orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field. Phys. Rev. A 77, 042309 (2008)ADSCrossRef
36.
Wu, L.A., Lidar, D.A.: Universal quantum logic from Zeeman and anisotropic exchange interactions. Phys. Rev. A 66, 062314 (2002)ADSCrossRef
37.
38.
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)
39.
Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)
40.
Vedral, V.: Modern Foundations of Quantum Optics. University of Leeds, Imperial College Press, Leeds (2005)CrossRefMATH
Metadata
Title
Quantum phase transition in the Dzyaloshinskii–Moriya interaction with inhomogeneous magnetic field: Geometric approach
Authors
G. Najarbashi
B. Seifi
Publication date
01-02-2017
Publisher
Springer US
Published in
Quantum Information Processing / Issue 2/2017
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-016-1505-7

Other articles of this Issue 2/2017

Quantum Information Processing 2/2017 Go to the issue

OriginalPaper

Characterizing error propagation in quantum circuits: the Isotropic Index

OriginalPaper

Overcoming experimental limitations in a nonlinear two-qubit gate through postselection

OriginalPaper

Cryptanalysis and improvement of a quantum private set intersection protocol

OriginalPaper

Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations

OriginalPaper

Post-Markovian dynamics of quantum correlations: entanglement versus discord

OriginalPaper

General monogamy relations of quantum entanglement for multiqubit W-class states