Skip to main content
Top
Published in: Quantum Information Processing 1/2019

01-01-2019

One-way deficit and quantum phase transitions in XY model and extended Ising model

Authors: Yao-Kun Wang, Yu-Ran Zhang, Heng Fan

Published in: Quantum Information Processing | Issue 1/2019

Log in

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

search-config
loading …

Abstract

Originating in questions regarding work extraction from quantum systems coupled to a heat bath, the quantum deficit, a kind of quantum correlations in addition to entanglement and quantum discord, links quantum thermodynamics with quantum information theory. In this paper, we investigate the one-way deficit of two adjacent spins in the bulk of the XY model and the extended Ising model. We find that the one-way deficit susceptibility is able to characterize quantum phase transitions in the XY model and even topological phase transitions in the extend Ising model. This study will enlighten extensive studies of quantum phase transitions from the perspective of quantum information processing and quantum computation, including finite-temperature phase transitions, topological phase transitions, and dynamical phase transitions in a variety of quantum many-body systems.

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!

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!

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!

Appendix
Available only for authorised users
Literature
1.
go back to reference Oppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002)MATHADS Oppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002)MATHADS
2.
go back to reference Horodecki, M., Horodecki, K., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U.: Local information as a resource in distributed quantum systems. Phys. Rev. Lett. 90, 100402 (2003)MathSciNetMATHADS Horodecki, M., Horodecki, K., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U.: Local information as a resource in distributed quantum systems. Phys. Rev. Lett. 90, 100402 (2003)MathSciNetMATHADS
3.
go back to reference Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)ADS Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)ADS
4.
go back to reference Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 062307 (2005)MATHADS Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 062307 (2005)MATHADS
5.
go back to reference Horodecki, M., Horodecki, P., Oppenheim, J.: Reversible transformations from pure to mixed states and the unique measure of information. Phys. Rev. A 67, 062104 (2003)MathSciNetADS Horodecki, M., Horodecki, P., Oppenheim, J.: Reversible transformations from pure to mixed states and the unique measure of information. Phys. Rev. A 67, 062104 (2003)MathSciNetADS
6.
go back to reference Streltsov, A., Kampermann, H., Bruß, D.: Quantum cost for sending entanglement. Phys. Rev. Lett. 108, 250501 (2012)ADS Streltsov, A., Kampermann, H., Bruß, D.: Quantum cost for sending entanglement. Phys. Rev. Lett. 108, 250501 (2012)ADS
7.
go back to reference Chuan, T.K., Maillard, J., Modi, K., Paterek, T., Paternostro, M., Piani, M.: Quantum discord bounds the amount of distributed entanglement. Phys. Rev. Lett. 109, 070501 (2012)ADS Chuan, T.K., Maillard, J., Modi, K., Paterek, T., Paternostro, M., Piani, M.: Quantum discord bounds the amount of distributed entanglement. Phys. Rev. Lett. 109, 070501 (2012)ADS
8.
go back to reference Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45–53 (2010)ADS Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45–53 (2010)ADS
9.
go back to reference Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008)MathSciNetMATHADS Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008)MathSciNetMATHADS
10.
go back to reference Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002)ADS Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002)ADS
11.
go back to reference Wu, L.-A., Sarandy, M.S., Lidar, D.A.: Quantum phase transitions and bipartite entanglement. Phys. Rev. Lett. 93, 250404 (2004)MathSciNetADS Wu, L.-A., Sarandy, M.S., Lidar, D.A.: Quantum phase transitions and bipartite entanglement. Phys. Rev. Lett. 93, 250404 (2004)MathSciNetADS
12.
go back to reference Orús, R., Wei, T.C.: Visualizing elusive phase transitions with geometric entanglement. Phys. Rev. B 82, 155120 (2010)ADS Orús, R., Wei, T.C.: Visualizing elusive phase transitions with geometric entanglement. Phys. Rev. B 82, 155120 (2010)ADS
13.
go back to reference Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)ADS Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)ADS
14.
go back to reference Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002)MathSciNetADS Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002)MathSciNetADS
15.
go back to reference Dillenschneider, R.: Quantum discord and quantum phase transition in spin chains. Phys. Rev. B 78, 224413 (2008)ADS Dillenschneider, R.: Quantum discord and quantum phase transition in spin chains. Phys. Rev. B 78, 224413 (2008)ADS
16.
go back to reference Zhang, X.Z., Guo, J.L.: Quantum correlation and quantum phase transition in the one-dimensional extended Ising model. Quantum Inf. Process. 16, 223 (2017)MathSciNetMATHADS Zhang, X.Z., Guo, J.L.: Quantum correlation and quantum phase transition in the one-dimensional extended Ising model. Quantum Inf. Process. 16, 223 (2017)MathSciNetMATHADS
17.
go back to reference Cui, J., Cao, J.P., Fan, H.: Entanglement-assisted local operations and classical communications conversion in quantum critical systems. Phys. Rev. A 85, 022338 (2012)ADS Cui, J., Cao, J.P., Fan, H.: Entanglement-assisted local operations and classical communications conversion in quantum critical systems. Phys. Rev. A 85, 022338 (2012)ADS
18.
go back to reference Cui, J., Gu, M., Kwek, L.C., Santos, M.F., Fan, H., Vedral, V.: Quantum phases with differing computational power. Nat. Commun. 3, 812 (2012)ADS Cui, J., Gu, M., Kwek, L.C., Santos, M.F., Fan, H., Vedral, V.: Quantum phases with differing computational power. Nat. Commun. 3, 812 (2012)ADS
19.
go back to reference Cui, J., Amico, L., Fan, H., Gu, M., Hamma, A., Vedral, V.: Local characterization of one-dimensional topologically ordered states. Phys. Rev. B 88, 125117 (2013)ADS Cui, J., Amico, L., Fan, H., Gu, M., Hamma, A., Vedral, V.: Local characterization of one-dimensional topologically ordered states. Phys. Rev. B 88, 125117 (2013)ADS
20.
go back to reference Franchini, F., Cui, J., Amico, L., Fan, H., Gu, M., Korepin, V., Kwek, L.C., Vedral, V.: Local convertibility and the quantum simulation of edge states in many-body systems. Phys. Rev. X 4, 041028 (2014) Franchini, F., Cui, J., Amico, L., Fan, H., Gu, M., Korepin, V., Kwek, L.C., Vedral, V.: Local convertibility and the quantum simulation of edge states in many-body systems. Phys. Rev. X 4, 041028 (2014)
21.
go back to reference Liu, S.Y., Quan, Q., Chen, J.J., Zhang, Y.R., Yang, W.L., Fan, H.: Phase diagram of quantum critical system via local convertibility of ground state. Sci. Rep. 6, 29175 (2016)ADS Liu, S.Y., Quan, Q., Chen, J.J., Zhang, Y.R., Yang, W.L., Fan, H.: Phase diagram of quantum critical system via local convertibility of ground state. Sci. Rep. 6, 29175 (2016)ADS
22.
go back to reference 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)ADS 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)ADS
23.
go back to reference Wen, X.G., Niu, Q.: Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces. Phys. Rev. B 41, 9377–9396 (1990)ADS Wen, X.G., Niu, Q.: Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces. Phys. Rev. B 41, 9377–9396 (1990)ADS
24.
go back to reference Wen, X.G.: Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons. Oxford University Press on Demand, Oxford (2004) Wen, X.G.: Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons. Oxford University Press on Demand, Oxford (2004)
25.
go back to reference Kitaev, A.Y.: Unpaired Majorana fermions in quantum wires. Phys. Uspekhi 44, 131 (2001)ADS Kitaev, A.Y.: Unpaired Majorana fermions in quantum wires. Phys. Uspekhi 44, 131 (2001)ADS
26.
27.
go back to reference Levin, M., Wen, X.G.: Detecting topological order in a ground state wave function. Phys. Rev. Lett. 96, 110405 (2006)ADS Levin, M., Wen, X.G.: Detecting topological order in a ground state wave function. Phys. Rev. Lett. 96, 110405 (2006)ADS
28.
go back to reference Li, H., Haldane, F.D.M.: Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states. Phys. Rev. Lett. 101, 010504 (2008)ADS Li, H., Haldane, F.D.M.: Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states. Phys. Rev. Lett. 101, 010504 (2008)ADS
29.
go back to reference Zhang, Y.R., Zeng, Y., Fan, H., You, J.Q., Nori, F.: Characterization of topological states via dual multipartite entanglement. Phys. Rev. Lett. 120, 250501 (2018)MathSciNetADS Zhang, Y.R., Zeng, Y., Fan, H., You, J.Q., Nori, F.: Characterization of topological states via dual multipartite entanglement. Phys. Rev. Lett. 120, 250501 (2018)MathSciNetADS
30.
go back to reference Zhang, G., Song, Z.: Topological characterization of extended quantum Ising models. Phys. Rev. Lett. 115, 177204 (2015)ADS Zhang, G., Song, Z.: Topological characterization of extended quantum Ising models. Phys. Rev. Lett. 115, 177204 (2015)ADS
31.
go back to reference Zhang, G., Li, C., Song, Z.: Majorana charges, winding numbers and Chern numbers in quantum Ising models. Sci. Rep. 7, 8176 (2017)ADS Zhang, G., Li, C., Song, Z.: Majorana charges, winding numbers and Chern numbers in quantum Ising models. Sci. Rep. 7, 8176 (2017)ADS
32.
go back to reference Streltsov, A., Kampermann, H., Bruß, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. 106, 160401 (2011)ADS Streltsov, A., Kampermann, H., Bruß, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. 106, 160401 (2011)ADS
33.
go back to reference Mukherjee, V., Divakaran, U., Dutta, A., Sen, D.: Quenching dynamics of a quantum XY spin-\(\frac{1}{2}\) chain in a transverse field. Phys. Rev. B 76, 174303 (2007)ADS Mukherjee, V., Divakaran, U., Dutta, A., Sen, D.: Quenching dynamics of a quantum XY spin-\(\frac{1}{2}\) chain in a transverse field. Phys. Rev. B 76, 174303 (2007)ADS
34.
go back to reference Garnerone, S., Jacobson, N.T., Haas, S., Zanardi, P.: Fidelity approach to the disordered quantum XY model. Phys. Rev. Lett. 102, 057205 (2009)ADS Garnerone, S., Jacobson, N.T., Haas, S., Zanardi, P.: Fidelity approach to the disordered quantum XY model. Phys. Rev. Lett. 102, 057205 (2009)ADS
35.
go back to reference Franchini, F., Its, A.R., Korepin, V.E.: Renyi entropy of the XY spin chain. J. Phys. A: Math. Theor. 41, 025302 (2008)MathSciNetMATHADS Franchini, F., Its, A.R., Korepin, V.E.: Renyi entropy of the XY spin chain. J. Phys. A: Math. Theor. 41, 025302 (2008)MathSciNetMATHADS
36.
go back to reference Liu, S.Y., Zhang, Y.R., Yang, W.L., Fan, H.: Global quantum discord and quantum phase transition in XY model. Ann. Phys. 362, 805–813 (2015)MathSciNetMATHADS Liu, S.Y., Zhang, Y.R., Yang, W.L., Fan, H.: Global quantum discord and quantum phase transition in XY model. Ann. Phys. 362, 805–813 (2015)MathSciNetMATHADS
37.
go back to reference Qin, W., Wang, C., Long, G.L.: High-dimensional quantum state transfer through a quantum spin chain. Phys. Rev. A 87, 012339 (2013)ADS Qin, W., Wang, C., Long, G.L.: High-dimensional quantum state transfer through a quantum spin chain. Phys. Rev. A 87, 012339 (2013)ADS
38.
go back to reference Pfeuty, P.: The one-dimensional Ising model with a transverse field. Ann. Phys. 57, 79–90 (1970)ADS Pfeuty, P.: The one-dimensional Ising model with a transverse field. Ann. Phys. 57, 79–90 (1970)ADS
39.
go back to reference Son, W., Amico, L., Plastina, F., Vedral, V.: Quantum instability and edge entanglement in the quasi-long-range order. Phys. Rev. A 79, 022302 (2009)ADS Son, W., Amico, L., Plastina, F., Vedral, V.: Quantum instability and edge entanglement in the quasi-long-range order. Phys. Rev. A 79, 022302 (2009)ADS
40.
go back to reference Wang, Y.K., Zhang, Y.R.: One-way deficit and quantum phase transitions in XX model. Int. J. Theor. Phys. 57, 363–370 (2018)MathSciNetMATH Wang, Y.K., Zhang, Y.R.: One-way deficit and quantum phase transitions in XX model. Int. J. Theor. Phys. 57, 363–370 (2018)MathSciNetMATH
41.
go back to reference Niu, Y.Z., Chung, S.B., Hsu, C.H., Mandal, I., Raghu, S., Chakravarty, S.: Majorana zero modes in a quantum Ising chain with longer-ranged interactions. Phys. Rev. B 85, 035110 (2012)ADS Niu, Y.Z., Chung, S.B., Hsu, C.H., Mandal, I., Raghu, S., Chakravarty, S.: Majorana zero modes in a quantum Ising chain with longer-ranged interactions. Phys. Rev. B 85, 035110 (2012)ADS
42.
go back to reference Vodola, D., Lepori, L., Ercolessi, E., Gorshkov, A.V., Pupillo, G.: Kitaev chains with long-range pairing. Phys. Rev. Lett. 113, 156402 (2014)ADS Vodola, D., Lepori, L., Ercolessi, E., Gorshkov, A.V., Pupillo, G.: Kitaev chains with long-range pairing. Phys. Rev. Lett. 113, 156402 (2014)ADS
43.
go back to reference Feng, X.Y., Zhang, G.M., Xiang, T.: Topological characterization of quantum phase transitions in a spin-1/2 model. Phys. Rev. Lett. 98, 087204 (2007)ADS Feng, X.Y., Zhang, G.M., Xiang, T.: Topological characterization of quantum phase transitions in a spin-1/2 model. Phys. Rev. Lett. 98, 087204 (2007)ADS
44.
go back to reference Qin, Y.Q., He, Y.Y., You, Y.Z., Lu, Z.Y., Sen, A., Sandvik, A.W., Xu, C.K., Meng, Z.Y.: Duality between the deconfined quantum-critical point and the bosonic topological transition. Phys. Rev. X 7, 031052 (2017) Qin, Y.Q., He, Y.Y., You, Y.Z., Lu, Z.Y., Sen, A., Sandvik, A.W., Xu, C.K., Meng, Z.Y.: Duality between the deconfined quantum-critical point and the bosonic topological transition. Phys. Rev. X 7, 031052 (2017)
45.
go back to reference Ye, B.L., Fei, S.M.: A note on one-way quantum deficit and quantum discord. Quantum Inf. Process. 15, 279–289 (2016)MathSciNetMATHADS Ye, B.L., Fei, S.M.: A note on one-way quantum deficit and quantum discord. Quantum Inf. Process. 15, 279–289 (2016)MathSciNetMATHADS
46.
go back to reference Luo, S.L.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)ADS Luo, S.L.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)ADS
47.
go back to reference Chiu, C.K., Teo, J.C.Y., Schnyder, A.P., Ryu, S.: Classification of topological quantum matter with symmetries. Rev. Mod. Phys. 88, 035005 (2016)ADS Chiu, C.K., Teo, J.C.Y., Schnyder, A.P., Ryu, S.: Classification of topological quantum matter with symmetries. Rev. Mod. Phys. 88, 035005 (2016)ADS
Metadata
Title
One-way deficit and quantum phase transitions in XY model and extended Ising model
Authors
Yao-Kun Wang
Yu-Ran Zhang
Heng Fan
Publication date
01-01-2019
Publisher
Springer US
Published in
Quantum Information Processing / Issue 1/2019
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-018-2132-2

Other articles of this Issue 1/2019

Quantum Information Processing 1/2019 Go to the issue