Decoherence factor in quantum phase transition

  • Hongting Song
  • Yu Pan
  • Yuanyuan MaoEmail author


As a fundamental quantity in quantum dynamics, decoherence factor reflects the influence on the system brought by the environment. In this work, we mainly investigate the dynamical behavior of decoherence factor in the quantum phase transition progresses, from the perspective of its phase information, amplitude information, real part information, and imaginary part information. Through two significant models, we show that most of these quantities can act as a witness of quantum phase transition phenomena and correctly reveal the locations of the critical points.


Quantum decoherence factor Quantum phase transition Quantum criticality 



  1. 1.
    Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  2. 2.
    Lieb, E., Schultz, T., Mattis, D.: Two soluble models of an antiferromagnetic chain. Ann. Phys. 16, 407 (1961)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Pfeuty, P.: The one-dimensional Ising model with a transverse field. Ann. Phys. 57, 79 (1970)ADSCrossRefGoogle Scholar
  4. 4.
    Barouch, E., McCoy, B.M.: Statistical mechanics of the XY model. III. Phys. Rev. A 3, 2137 (1971)ADSCrossRefGoogle Scholar
  5. 5.
    Haviland, D.B., Liu, Y., Goldman, A.M.: Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989)ADSCrossRefGoogle Scholar
  6. 6.
    van der Zant, H.S.J., Fritschy, F.C., Elion, W.E., Geerligs, L.J., Mooij, J.E.: Field-induced superconductor-to-insulator transition in Josephson junction arrays. Phys. Rev. Lett. 69, 2971–2974 (1992)ADSCrossRefGoogle Scholar
  7. 7.
    Greiner, M., Mandel, O., Esslinger, T., Hansch, T.W., Bloch, I.: Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    Landau, L.D., Lifschitz, E.M.: Statistical Physics: Course of Theoretical Physics. Pergamon, London (1958)Google Scholar
  9. 9.
    Resnick, D.J., Garland, J.C., Boyd, J.T., Shoemaker, S., Newrock, R.S.: Kosterlitz–Thouless transition in proximity-coupled superconducting arrays. Phys. Rev. Lett. 47, 1542 (1981)ADSCrossRefGoogle Scholar
  10. 10.
    Kosterlitz, J.M., Thouless, D.J.: Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C Solid State Phys. 6, 1181 (1973)ADSCrossRefGoogle Scholar
  11. 11.
    Wen, X.G.: Quantum Field Theory of Many-Body Systems. Oxford University Press, New York (2004)Google Scholar
  12. 12.
    Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    Wu, L.-A., Sarandy, M.S., Lidar, D.A.: Quantum phase transitions and bipartite entanglement. Phys. Rev. Lett. 93, 250404 (2004)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Lu, X.-M., Sun, Z., Wang, X., Zanardi, P.: Operator fidelity susceptibility, decoherence, quantum criticality. Phys. Rev. A 78, 032309 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Kwok, H.-M., Ning, W.-Q., Gu, S.-J., Lin, H.-Q.: Quantum criticality of the Lipkin–Meshkov–Glick model in terms of fidelity susceptibility. Phys. Rev. E 78, 032103 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    Gu, S.-J.: Fidelity approach to quantum phase transitions. Int. J. Mod. Phys. B 24, 4371 (2010)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Luo, D.-W., Xu, J.-B.: Trace distance and scaling behavior of a coupled cavity lattice at finite temperature. Phys. Rev. A 87, 013801 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    Ma, J., Wang, X.: Fisher information and spin squeezing in the Lipkin–Meshkov–Glick model. Phys. Rev. A 80, 012318 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    Liu, W.-F., Ma, J., Wang, X.: Quantum Fisher information and spin squeezing in the ground state of the XY model. J. Phys. A Math. Theor. 46, 045302 (2013)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Wang, T.-L., Wu, L.-N., Yang, W., Jin, G.-R., Lambert, N., Nori, F.: Quantum Fisher information as a signature of the superradiant quantum phase transition. New J. Phys. 16, 063039 (2014)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Song, H., Luo, S., Fu, S.: Quantum criticality from Fisher information. Quantum Inf. Process. 16, 91 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    Quan, H.T., Song, Z., Liu, X.F., Zanardi, P., Sun, C.P.: Decay of Loschmidt echo enhanced by quantum criticality. Phys. Rev. Lett. 96, 140604 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    Zanardi, P., Quan, H.T., Wang, X., Sun, C.P.: Mixed-state fidelity and quantum criticality at finite temperature. Phys. Rev. A 75, 032109 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. 105, 095702 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    Li, Y.C., Lin, H.Q.: Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction. Phys. Rev. A 83, 052323 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Zanardi, P., Paris, M.G.A., Venuti, L.C.: Quantum criticality as a resource for quantum estimation. Phys. Rev. A 78, 042105 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Invernizzi, C., Korbman, M., Venuti, L.C., Paris, M.G.A.: Optimal quantum estimation in spin systems at criticality. Phys. Rev. A 78, 042106 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    Salvatori, G., Mandarino, A., Paris, M.G.A.: Quantum metrology in Lipkin–Meshkov–Glick critical systems. Phys. Rev. A 90, 022111 (2014)ADSCrossRefGoogle Scholar
  30. 30.
    Fernández-Lorenzo, S., Porras, D.: Quantum sensing close to a dissipative phase transition: symmetry breaking and criticality as metrological resources. Phys. Rev. A 96, 013817 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    Jaseem, N., Omkar, S., Shaji, A.: Quantum critical environment assisted quantum magnetometer. J. Phys. A Math. Theor. 51, 17 (2018)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)zbMATHGoogle Scholar
  33. 33.
    Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Damski, B., Quan, H.T., Zurek, W.H.: Critical dynamics of decoherence. Phys. Rev. A 83, 062104 (2011)ADSCrossRefGoogle Scholar
  35. 35.
    Karpat, G., Çakmak, B., Fanchini, F.F.: Quantum coherence and uncertainty in the anisotropic XY chain. Phys. Rev. B 90, 104431 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    Chen, J.-J., Cui, J., Zhang, Y.-R., Fan, H.: Coherence susceptibility as a probe of quantum phase transitions. Phys. Rev. A 94, 022112 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    Malvezzi, A.L., Karpat, G., Çakmak, B., Fanchini, F.F., Debarba, T., Vianna, R.O.: Quantum correlations and coherence in spin-1 Heisenberg chains. Phys. Rev. B 93, 184428 (2016)ADSCrossRefGoogle Scholar
  38. 38.
    Zhang, G.-Q., Xu, J.-B.: Quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction and quantum phase transition. J. Phys. A Math. Theor. 50, 265303 (2017)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93, 99 (1954)ADSCrossRefGoogle Scholar
  40. 40.
    Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    Baumann, K., Guerlin, C., Brennecke, F., Esslinger, T.: Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301 (2010)ADSCrossRefGoogle Scholar
  42. 42.
    Fröhlich, H.: Theory of the superconducting state. I. The ground state at the absolute zero of temperature. Phys. Rev. 79, 85 (1950)CrossRefGoogle Scholar
  43. 43.
    Nakajima, S.: Perturbation theory in statistical mechanics. Adv. Phys. 4, 363 (1955)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Holstein, T., Primakoff, H.: Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58, 1098 (1940)ADSCrossRefGoogle Scholar
  45. 45.
    Huang, J.-F., Li, Y., Liao, J.-Q., Kuang, L.-M., Sun, C.P.: Dynamic sensitivity of photon-dressed atomic ensemble with quantum criticality. Phys. Rev. A 80, 063829 (2009)ADSCrossRefGoogle Scholar
  46. 46.
    Yuan, J.-B., Kuang, L.-M.: Quantum-discord amplification induced by a quantum phase transition via a cavity-Bose–Einstein-condensate system. Phys. Rev. A 87, 024101 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    Wu, W., Xu, J.-B.: Geometric phase, quantum Fisher information, geometric quantum correlation and quantum phase transition in the cavity-Bose–Einstein-condensate system. Quantum Infor. Process. 15, 3695–3709 (2016)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Emary, C., Brandes, T.: Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model. Phys. Rev. Lett. 90, 044101 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    Emary, C., Brandes, T.: Chaos and the quantum phase transition in the Dicke model. Phys. Rev. E 67, 066203 (2003)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    Yuan, Z.-G., Zhang, P., Li, S.-S.: Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition. Phys. Rev. A 76, 042118 (2007)ADSCrossRefGoogle Scholar
  51. 51.
    Li, Y.-C., Lin, H.-Q., Xu, J.-B.: Dynamics of correlations and scaling behaviors in a spin-chain environment. Europhys. Lett. 100, 20002 (2012)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Qian Xuesen Laboratory of Space TechnologyChina Academy of Space TechnologyBeijingPeople’s Republic of China
  2. 2.Institute of Cyber-Systems and ControlZhejiang UniversityHangzhouPeople’s Republic of China
  3. 3.Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhenPeople’s Republic of China
  4. 4.Naturwissenschaftlich-Technische FakultätUniversität SiegenSiegenGermany

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