Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Entanglement entropy in the semi-classical approximation as an observable for investigating shape phase transition in nuclei

Document Type : Research Paper

Authors

M. Ghapanvari 1
M.A. Jafarizadeh 2
M. Seidi 3
N. Amiri 4

1 Plasma and Nuclear Fusion Research School, Nuclear Science and Technology Research Institute, AEOI, P.O. Box: 14399-51113, Tehran – Iran

2 Theoretical Group, Faculty of Physics, Tabriz University, P.O. Box: 51664, Tabriz – Iran

3 Department of Physics, Faculty of Sciences, Ilam University, P.O.Box: 69315-516, Ilam – Iran

4 Nuclear Group, Faculty of Physics, Tabriz University, P.O. Box: 51664, Tabriz – Iran

https://doi.org/10.24200/nst.2023.1609
Abstract
In this paper, quantum phase transitions and nuclear structure were investigated based on quantum entanglement. One of the measures for entanglement between two bodies is the von Neumann entropy, which is considered a suitable criterion for examining entanglement. The entanglement entropy of s-d bosons within the framework of the Interacting Boson Model (IBM) is investigated using the consistent-Q formalism and semiclassical approximation. This research presents a method for deriving the entanglement entropy in the dynamical symmetry limits of the IBM, including transition regions between different shapes. By utilizing the entanglement effect, the quantum phase transition was described, and the entanglement behavior of s and d bosons was investigated in various regions of the Castan triangle. A method for determining entropy in the IBM model using the semiclassical approximation was presented. The results showed that entanglement entropy values are sensitive to phase changes and can be a powerful tool for detecting quantum phase transitions in nuclei.

Highlights

  1. Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Physical Review. 1935;47(10):777.

 

  1. 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. Physical Review Letters. 1993;70(13):1895.

 

  1. Ekert A.K. Quantum cryptography based on Bell’s theorem. Physical Review Letters. 1991;67(6):661.

 

  1. Ekert A, Jozsa R. Quantum computation and Shor's factoring algorithm. Reviews of Modern Physics. 1996;68(3):733.

 

  1. Pichler T, Dalmonte M, Rico E, Zoller P, Montangero S. Real-time dynamics in U(1) lattice gauge theories with tensor networks. Physical Review X. 2016;6(1):011023.

 

  1. Cloët I.C, Dietrich M.R, Arrington J, Bazavov A, Bishof M, Freese A, Zohar E. Opportunities for Nuclear Physics & Quantum Information Science. arXiv preprint arXiv:1903.05453. 2019.

 

  1. Ring P, Schuck P. The nuclear many-body problem. Springer Science & Business Media. 2004.‏

 

  1. Kaplan D.B, Klco N, Roggero A. Ground states via spectral combing on a quantum computer. arXiv preprint arXiv:1709.08250. 2017.

 

  1. Roggero A, Carlson J. Linear response on a quantum computer. arXiv preprint arXiv:1804.01505. 2018.

 

  1. Lamm H, Lawrence S. Simulation of nonequilibrium dynamics on a quantum computer. Physical Review Letters. 2018;121(17):170501.

 

  1. Kaplan D.B, Klco N, Roggero A. Ground states via spectral combing on a quantum computer. arXiv preprint arXiv:1709.08250. 2017.‏

 

  1. Peruzzo A, McClean J, Shadbolt P, Yung M.H, Zhou X.Q, Love P.J, O’brien J.L. A variational eigenvalue solver on a photonic quantum processor. Nature Communications. 2014;5(1):1-7.‏

 

  1. McClean J.R, Romero J, Babbush R, Aspuru-Guzik A. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics. 2016;18(2):023023.‏

 

  1. Chatzidimitriou-Dreismann C.A, Redah T.A, Streffer R.M.F, Mayers J. Anomalous Deep Inelastic Neutron Scattering from Liquid H2O-D2O: Evidence of Nuclear Quantum Entanglement. Physical Review Letters. 1997;79(15):2839.‏

 

  1. Bender M, Bernard R, Bertsch G, Chiba S, Dobaczewski J, Dubray N, Åberg S. Future of nuclear fission theory. Journal of Physics G: Nuclear and Particle Physics. 2020;47(11):113002.

 

  1. Schunck N, Robledo L.M. Microscopic theory of nuclear fission: a review. Reports on Progress in Physics. 2016;79(11):116301.‏

 

  1. Schunck N, Duke D, Carr H, Knoll A. Description of induced nuclear fission with Skyrme energy functionals: Static potential energy surfaces and fission fragment properties. Physical Review C. 2014;90(5):054305.‏

 

  1. Bulgac A, Jin S. Dynamics of fragmented condensates and macroscopic entanglement. Physical Review Letters. 2017;119(5):052501.‏

 

  1. Bulgac A, Jin S, Magierski P, Roche K.J, Stetcu I. Microscopic theory of nuclear fission. arXiv preprint arXiv:1704.00689. 2017.‏

 

  1. Sadhukhan J, Zhang C, Nazarewicz W, Schunck N. Formation and distribution of fragments in the spontaneous fission of 240 Pu. Physical Review C. 2017;96(6):061301.

 

  1. Verriere M, Schunck N, Kawano T. Number of particles in fission fragments. Physical Review C. 2019;100(2):024612.‏

 

  1. Bertulani C.A, Hussein M.S, Verde G. Blurred femtoscopy in two-proton decay. Physics Letters B. 2008;666(1):86-90.‏

 

  1. Bertulani C.A. Fingerprints of entangled states in reactions with rare isotopes. Journal of Physics G: Nuclear and Particle Physics. 2003;29(4):769.‏

 

  1. Lello L, Boyanovsky D, Holman R. Entanglement entropy in particle decay. Journal of High Energy Physics. 2013;2013(11):116.

 

  1. Dulski K, Bass S.D, Chhokar J, Chug N, Curceanu C, Czerwiński E, Moskal P. First observation of ortho-positronium with the J-PET tomograph. arXiv preprint arXiv:2006.07467. 2020.‏

 

  1. Raj J, Silarski M. Study of the time reversal symmetry in the decay of ortho-Positronium atoms using the J-PET detector. In EPJ Web of Conferences. EDP Sciences. 2019;199:05015.

 

  1. Moskal P, Krawczyk N, Hiesmayr B.C, Bała M, Curceanu C, Czerwiński E, Zgardzińska B. Feasibility studies of the polarization of photons beyond the optical wavelength regime with the J-PET detector. The European Physical Journal C. 2018;78(11):1-9.‏

 

  1. Czerwiński E, Curceanu C, Dulski K, Gajos A, Gorgol M, Heczko A, Moskal P. Studies of discrete symmetries in decays of positronium atoms. In EPJ Web of Conferences. EDP Sciences. 2018;181:01019.

 

  1. Horodecki R, Horodecki P, Horodecki M, Horodecki K. Quantum entanglement. Reviews of Modern Physics. 2009;81(2):865.‏

 

  1. Gühne O, Tóth G. Entanglement detection. Physics Reports. (2009);474(1-6):1-75.‏

 

  1. Amico L, Fazio R, Osterloh A, Vedral V. Entanglement in many-body systems. Reviews of Modern Physics. 2008;80(2):517.‏

 

  1. Benatti F, Floreanini R, Franchini F, Marzolino U. Entanglement in indistinguishable particle systems. Physics Reports. 2020.‏

 

  1. Jafarizadeh M.A, Ghapanvari M, Amiri N. Entanglement entropy as a signature of a quantum phase transition in nuclei in the framework of the interacting boson model and interacting boson-fermion model. Physical Review C. 2022;105(1):014307.‏

 

  1. Cejnar P, Jolie J, Casten R.F. Quantum phase transitions in the shapes of atomic nuclei. Reviews of Modern Physics. 2010;82(3):2155.‏

 

  1. Perelomov A. Standard system of coherent states related to the heisenberg-weyl group: One degree of freedom. In Generalized Coherent States and Their Applications. Springer, Berlin, Heidelberg. 1986;7–39.

Keywords

Quantum phase transition
Quantum entanglement
Boson interaction model (IBM)
Entropy
Semi-classical approximation
  1. Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Physical Review. 1935;47(10):777.

 

  1. 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. Physical Review Letters. 1993;70(13):1895.

 

  1. Ekert A.K. Quantum cryptography based on Bell’s theorem. Physical Review Letters. 1991;67(6):661.

 

  1. Ekert A, Jozsa R. Quantum computation and Shor's factoring algorithm. Reviews of Modern Physics. 1996;68(3):733.

 

  1. Pichler T, Dalmonte M, Rico E, Zoller P, Montangero S. Real-time dynamics in U(1) lattice gauge theories with tensor networks. Physical Review X. 2016;6(1):011023.

 

  1. Cloët I.C, Dietrich M.R, Arrington J, Bazavov A, Bishof M, Freese A, Zohar E. Opportunities for Nuclear Physics & Quantum Information Science. arXiv preprint arXiv:1903.05453. 2019.

 

  1. Ring P, Schuck P. The nuclear many-body problem. Springer Science & Business Media. 2004.‏

 

  1. Kaplan D.B, Klco N, Roggero A. Ground states via spectral combing on a quantum computer. arXiv preprint arXiv:1709.08250. 2017.

 

  1. Roggero A, Carlson J. Linear response on a quantum computer. arXiv preprint arXiv:1804.01505. 2018.

 

  1. Lamm H, Lawrence S. Simulation of nonequilibrium dynamics on a quantum computer. Physical Review Letters. 2018;121(17):170501.

 

  1. Kaplan D.B, Klco N, Roggero A. Ground states via spectral combing on a quantum computer. arXiv preprint arXiv:1709.08250. 2017.‏

 

  1. Peruzzo A, McClean J, Shadbolt P, Yung M.H, Zhou X.Q, Love P.J, O’brien J.L. A variational eigenvalue solver on a photonic quantum processor. Nature Communications. 2014;5(1):1-7.‏

 

  1. McClean J.R, Romero J, Babbush R, Aspuru-Guzik A. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics. 2016;18(2):023023.‏

 

  1. Chatzidimitriou-Dreismann C.A, Redah T.A, Streffer R.M.F, Mayers J. Anomalous Deep Inelastic Neutron Scattering from Liquid H2O-D2O: Evidence of Nuclear Quantum Entanglement. Physical Review Letters. 1997;79(15):2839.‏

 

  1. Bender M, Bernard R, Bertsch G, Chiba S, Dobaczewski J, Dubray N, Åberg S. Future of nuclear fission theory. Journal of Physics G: Nuclear and Particle Physics. 2020;47(11):113002.

 

  1. Schunck N, Robledo L.M. Microscopic theory of nuclear fission: a review. Reports on Progress in Physics. 2016;79(11):116301.‏

 

  1. Schunck N, Duke D, Carr H, Knoll A. Description of induced nuclear fission with Skyrme energy functionals: Static potential energy surfaces and fission fragment properties. Physical Review C. 2014;90(5):054305.‏

 

  1. Bulgac A, Jin S. Dynamics of fragmented condensates and macroscopic entanglement. Physical Review Letters. 2017;119(5):052501.‏

 

  1. Bulgac A, Jin S, Magierski P, Roche K.J, Stetcu I. Microscopic theory of nuclear fission. arXiv preprint arXiv:1704.00689. 2017.‏

 

  1. Sadhukhan J, Zhang C, Nazarewicz W, Schunck N. Formation and distribution of fragments in the spontaneous fission of 240 Pu. Physical Review C. 2017;96(6):061301.

 

  1. Verriere M, Schunck N, Kawano T. Number of particles in fission fragments. Physical Review C. 2019;100(2):024612.‏

 

  1. Bertulani C.A, Hussein M.S, Verde G. Blurred femtoscopy in two-proton decay. Physics Letters B. 2008;666(1):86-90.‏

 

  1. Bertulani C.A. Fingerprints of entangled states in reactions with rare isotopes. Journal of Physics G: Nuclear and Particle Physics. 2003;29(4):769.‏

 

  1. Lello L, Boyanovsky D, Holman R. Entanglement entropy in particle decay. Journal of High Energy Physics. 2013;2013(11):116.

 

  1. Dulski K, Bass S.D, Chhokar J, Chug N, Curceanu C, Czerwiński E, Moskal P. First observation of ortho-positronium with the J-PET tomograph. arXiv preprint arXiv:2006.07467. 2020.‏

 

  1. Raj J, Silarski M. Study of the time reversal symmetry in the decay of ortho-Positronium atoms using the J-PET detector. In EPJ Web of Conferences. EDP Sciences. 2019;199:05015.

 

  1. Moskal P, Krawczyk N, Hiesmayr B.C, Bała M, Curceanu C, Czerwiński E, Zgardzińska B. Feasibility studies of the polarization of photons beyond the optical wavelength regime with the J-PET detector. The European Physical Journal C. 2018;78(11):1-9.‏

 

  1. Czerwiński E, Curceanu C, Dulski K, Gajos A, Gorgol M, Heczko A, Moskal P. Studies of discrete symmetries in decays of positronium atoms. In EPJ Web of Conferences. EDP Sciences. 2018;181:01019.

 

  1. Horodecki R, Horodecki P, Horodecki M, Horodecki K. Quantum entanglement. Reviews of Modern Physics. 2009;81(2):865.‏

 

  1. Gühne O, Tóth G. Entanglement detection. Physics Reports. (2009);474(1-6):1-75.‏

 

  1. Amico L, Fazio R, Osterloh A, Vedral V. Entanglement in many-body systems. Reviews of Modern Physics. 2008;80(2):517.‏

 

  1. Benatti F, Floreanini R, Franchini F, Marzolino U. Entanglement in indistinguishable particle systems. Physics Reports. 2020.‏

 

  1. Jafarizadeh M.A, Ghapanvari M, Amiri N. Entanglement entropy as a signature of a quantum phase transition in nuclei in the framework of the interacting boson model and interacting boson-fermion model. Physical Review C. 2022;105(1):014307.‏

 

  1. Cejnar P, Jolie J, Casten R.F. Quantum phase transitions in the shapes of atomic nuclei. Reviews of Modern Physics. 2010;82(3):2155.‏

 

  1. Perelomov A. Standard system of coherent states related to the heisenberg-weyl group: One degree of freedom. In Generalized Coherent States and Their Applications. Springer, Berlin, Heidelberg. 1986;7–39.

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