Abstract
Identification of quantum phase transitions has been a long standing issue in quantum systems. In this work, we study the renormalization of Wigner–Yanase skew information in XY spin chain and compare its relation with cost of energy quantum correlation near the critical point. This study is presented by implementing the quantum renormalization group (RG) technique. We apply the (RG) method to examine existing phase transition in XY spin chain by using the cost of energy quantum correlations and Wigner–Yanase skew information. We demonstrate that cost of energy quantum can provide crucial information about quantum phase transitions as well as quantum correlations.
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References
M. Kargarian, R. Jafari, A. Langari, Phys. Rev. A 76, 06030 (2007)
M. Kargarian, R. Jafari, A. Langari, Phys. Rev. A 77, 032346 (2008)
A. Langari, F. Pollmann, M. Siahatgar, J. Phys, Condens. Matter 25, 406002 (2013)
Y.L. Xu, X.M. Kong, Z.Q. Liu, C.Y. Wang, Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice. Physica A 446, 217 (2016)
A. Osterloh, L. Amico, G. Falci, R. Fazio, Scaling of entanglement close to a quantum phase transitions. Nature 416, 608 (2002)
L. Lima, Effect of spin-phonon coupling on quantum correlation in the spin-1 XY model. Solid State Commun. 332, 114323 (2021)
L.S. Lima, Influence of Dzyaloshinskii–Moriya interaction and external fields on quantum entanglement in half-integer spin one-dimensional antiferromagnets. Eur. Phys. J. D 73(11), 1–7 (2019)
A.R. Its, B.-Q. Jin, V.E. Korepin, Entanglement in the XY spin chain. J. Phys. A Math. Gen. 38(13), 2975 (2005)
P. Calabrese, J. Cardy, Entanglement entropy and quantum field theory. J. Stat. Mech. Theory Exp. 2004(06), P06002 (2004)
S. Haddadi, M. Ghominejad, A. Akhound, M.R. Pourkarimi, Entropic uncertainty relation and quantum coherence under Ising model with Dzyaloshinskii–Moriya interaction. Laser Phys. Lett. 18(8), 085204 (2021)
S. Haseli, S. Haddadi, M.R. Pourkarimi, Entropic uncertainty lower bound for a two-qubit system coupled to a spin chain with Dzyaloshinskii–Moriya interaction. Opt. Quantum Electron. 52(10), 1–14 (2020)
F. Mirmasoudi, S. Ahadpour, J. Vahedi, S. Mahdavifar, The Loschmidt-echo dynamics in a quantum chaos model. Phys. Scr. 94(5), 055207 (2019)
S. Moshfegh, A. Ashouri, S. Mahdavifar, J. Vahedi, Integrable-chaos crossover in the spin-1/ 2 xxz chain with cluster interaction. Phys. A Stat. Mech. Appl. 516, 502–508 (2019)
A. Ashouri, S. Mahdavifar, G. Misguich, J. Vahedi, Concurrence and quantum discord in the eigenstates of chaotic and integrable spin chains. Ann. Phys. 532(8), 1900515 (2020)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90(22), 227902 (2003)
T. Werlang, C. Trippe, G.A.P. Ribeiro, G. Rigolin, Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. 105, 095702 (2010)
H. Ollivier, W. Zurek, Phys. Rev. Lett 88, 017901 (2001)
M. Ali, A.R.P. Rau, G. Alber, Phys. Rev. A 81, 042105 (2010)
X.X. Zhang, H.R. Li, The renormalization of geometric quantum discord in the transverse Ising model. Mod. Phys. Lett. B 29, 1550002 (2015)
P. Zanardi, N. Paunkovic, Ground state overlap and quantum phase transitions. Phys. Rev. E 74, 031123 (2006)
G.Q. Zhang, J.B. Xu, Quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction and quantum phase transition. J. Phys. A Math. Theor. 50, 13 (2017)
N. Behzadi, E. Soltani, E. Faizi, Thermodynamic cost of creating global quantum discord and local quantum uncertainty. Int. J. Theor. Phys. 57(10), 3207–3214 (2018)
K. Maruyama, F. Nori, V. Vedral, Colloquium: the physics of Maxwell’s demon and information. Rev. Mod. Phys. 81(1), 1 (2009)
M. Horodecki, J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics. Nat. Commun. 4(1), 1–6 (2013)
L. Del Rio, J. Åberg, R. Renner, O. Dahlsten, V. Vedral, The thermodynamic meaning of negative entropy. Nature 474(7349), 61–63 (2011)
M. Horodecki, J. Oppenheim, (Quantumness in the context of) resource theories. Int. J. Mod. Phys. B 27(01n03), 1345019 (2013)
M. Huber, M. Perarnau-Llobet, K.V. Hovhannisyan, P. Skrzypczyk, C. Klöckl, N. Brunner, A. Acín, Thermodynamic cost of creating correlations. New J. Phys. 17(6), 065008 (2015)
M. A. Nielsen, I. Chuang, Quantum computation and quantum information (2002)
A.K. Ekert, Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)
S. Mirzaei, A.R. Akbarieh, Quantum teleportation via entangled state of light in Schwarzschild black hole. Int. J. Theor. Phys. 59(11), 3583–3592 (2020)
C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895 (1993)
C.H. Bennett, S.J. Wiesner, Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69(20), 2881 (1992)
S. Ahadpour, F. Mirmasoudi, Super dense coding in one-axis twisting model. Rev. Mex. Fís. 66(3 May–Jun), 356–363 (2020)
A. Barenco, A.K. Ekert, Dense coding based on quantum entanglement. J. Mod. Opt. 42(6), 1253–1259 (1995)
S.L. Braunstein, H.J. Kimble, Dense coding for continuous variables, in Quantum Information with Continuous Variables (Springer, 2000), pp. 95–103
S. Bose, M.B. Plenio, V. Vedral, Mixed state dense coding and its relation to entanglement measures. J. Mod. Opt. 47(2–3), 291–310 (2000)
F. Mirmasoudi, S. Ahadpour, Dynamics of super quantum discord and optimal dense coding in quantum channels. J. Phys. A Math. Theor. 51(34), 345302 (2018)
F. Mirmasoudi, S. Ahadpour, Application quantum renormalization group to optimal dense coding in transverse Ising model. Phys. A Stat. Mech. Appl. 515, 232–239 (2019)
K. Mattle, H. Weinfurter, P.G. Kwiat, A. Zeilinger, Dense coding in experimental quantum communication. Phys. Rev. Lett. 76(25), 4656 (1996)
J.I. Latorre, E. Rico, G. Vidal, Ground state entanglement in quantum spin chains. arXiv:quant-ph/0304098 (2003)
J. Latorre, A. Riera, A short review on entanglement in quantum spin systems. J. Phys. Math. Theor. 42(50), 504002 (2009)
S. Haddadi, M. Bohloul, A brief overview of bipartite and multipartite entanglement measures. Int. J. Theor. Phys. 57(12), 3912–3916 (2018)
M.-L. Hu, X. Hu, J. Wang, Y. Peng, Y.-R. Zhang, H. Fan, Quantum coherence and geometric quantum discord. Phys. Rep. 762, 1–100 (2018)
S. Szalay, Multipartite entanglement measures. Phys. Rev. A 92(4), 042239 (2015)
Y. Khedif, S. Haddadi, M.R. Pourkarimi, M. Daoud, Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions. Mod. Phys. Lett. A 36(29), 2150209 (2021)
M.G. Paris, Quantum estimation for quantum technology. Int. J. Quantum Inf. 7(supp01), 125–137 (2009)
S. Luo, S. Fu, Geometric measure of quantum discord. Phys. Rev. A 82(3), 034302 (2010)
M. Kargarian, R. Jafari, A. Langari, Renormalization of entanglement in the anisotropic Heisenberg (x x z) model. Phys. Rev. A 77(3), 032346 (2008)
E.P. Wigner, M.M. Yanase, Information contents of distributions, in Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics (Springer, 1997), pp. 452–460
D. Girolami, T. Tufarelli, G. Adesso, Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110(24), 240402 (2013)
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Ahadpour, S., Mirmasoudi, F. Cost of Energy Quantum Correlation in a Spin Model. J Low Temp Phys 207, 1–10 (2022). https://doi.org/10.1007/s10909-022-02692-1
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DOI: https://doi.org/10.1007/s10909-022-02692-1
Keywords
- Quantum phase transition
- Wigner–Yanase skew information
- Quantum renormalization group
- Cost of energy quantum correlation