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Erschienen in: Quantum Information Processing 11/2015

01.11.2015

Quantum phase transition in dimerised spin-1/2 chains

verfasst von: Aparajita Das, Sreeparna Bhadra, Sonali Saha

Erschienen in: Quantum Information Processing | Ausgabe 11/2015

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Abstract

Quantum phase transition in dimerised antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical (or critical like) points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs too in the same dimer chain. Though closed dimerised isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.

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Literatur
1.
Zurück zum Zitat Sachdev, S.: Quantum Phase Transitions. Cambridge UniversityPress, Cambridge (1999) Sachdev, S.: Quantum Phase Transitions. Cambridge UniversityPress, Cambridge (1999)
2.
Zurück zum Zitat Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)CrossRefADS Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)CrossRefADS
3.
Zurück zum Zitat Zhou, L., Song, H.S., Guo, Y.Q., Li, C.: Enhanced thermal entanglement in an anisotropic Heisenberg XYZ chain. Phy. Rev. A 68, 024301 (2003)CrossRefADS Zhou, L., Song, H.S., Guo, Y.Q., Li, C.: Enhanced thermal entanglement in an anisotropic Heisenberg XYZ chain. Phy. Rev. A 68, 024301 (2003)CrossRefADS
5.
Zurück zum Zitat Bennett, C.H., Brassard, G., Crepeau, 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, 1895–1899 (1993)MathSciNetCrossRefADSMATH Bennett, C.H., Brassard, G., Crepeau, 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, 1895–1899 (1993)MathSciNetCrossRefADSMATH
6.
Zurück zum Zitat Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996)MathSciNetCrossRefADS Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996)MathSciNetCrossRefADS
7.
Zurück zum Zitat Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)CrossRefMATH Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)CrossRefMATH
8.
Zurück zum Zitat Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998)CrossRefADS Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998)CrossRefADS
9.
Zurück zum Zitat Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)CrossRefADS Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)CrossRefADS
10.
Zurück zum Zitat Burkard, G., Loss, D., DiVincenzo, D.P.: Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070–2078 (1999)CrossRefADS Burkard, G., Loss, D., DiVincenzo, D.P.: Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070–2078 (1999)CrossRefADS
11.
Zurück zum Zitat Imamoglu, A., Awschalom, D.D., Burkard, G., DiVincenzo, D.P., Loss, D., Sherwin, M., Small, A.: Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83, 4204–4207 (1999)CrossRefADS Imamoglu, A., Awschalom, D.D., Burkard, G., DiVincenzo, D.P., Loss, D., Sherwin, M., Small, A.: Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83, 4204–4207 (1999)CrossRefADS
12.
Zurück zum Zitat Nielsen, M.: Quantum information theory. Ph.D. thesis, University of New Mexico (1998) Nielsen, M.: Quantum information theory. Ph.D. thesis, University of New Mexico (1998)
13.
Zurück zum Zitat Wang, X.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313 (2001)CrossRefADS Wang, X.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313 (2001)CrossRefADS
14.
Zurück zum Zitat 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)CrossRefADS 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)CrossRefADS
15.
Zurück zum Zitat Sen, A., Sen, U., Lewenstein, M.: Dynamical phase transitions and temperature-induced quantum correlations in an infinite spin chain. Phys. Rev. A 72, 052319 (2005)CrossRefADS Sen, A., Sen, U., Lewenstein, M.: Dynamical phase transitions and temperature-induced quantum correlations in an infinite spin chain. Phys. Rev. A 72, 052319 (2005)CrossRefADS
16.
Zurück zum Zitat Sun, Y., Chen, Y., Chen, H.: Thermal entanglement in the two-qubit Heisenberg XY model under a non uniform external magnetic field. Phys. Rev. A 68, 044301 (2003)CrossRefADS Sun, Y., Chen, Y., Chen, H.: Thermal entanglement in the two-qubit Heisenberg XY model under a non uniform external magnetic field. Phys. Rev. A 68, 044301 (2003)CrossRefADS
17.
Zurück zum Zitat Terzis, A.F., Paspalakis, E.: Entanglement in a two-qubit Ising model under a site-dependent external magnetic field. Phys. Lett. A 333, 438–445 (2004)CrossRefADSMATH Terzis, A.F., Paspalakis, E.: Entanglement in a two-qubit Ising model under a site-dependent external magnetic field. Phys. Lett. A 333, 438–445 (2004)CrossRefADSMATH
18.
Zurück zum Zitat Gong, S.S., Su, G.: Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. Phys. Rev. A 80, 012323 (2009)CrossRefADS Gong, S.S., Su, G.: Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. Phys. Rev. A 80, 012323 (2009)CrossRefADS
19.
Zurück zum Zitat Plekhanov, E., Avella, A., Mancini, F.: Thermal entanglement in one- dimensional Heisenberg quantum spin chains under magnetic fields. Phys. B 403, 1282–1283 (2008)CrossRefADS Plekhanov, E., Avella, A., Mancini, F.: Thermal entanglement in one- dimensional Heisenberg quantum spin chains under magnetic fields. Phys. B 403, 1282–1283 (2008)CrossRefADS
20.
Zurück zum Zitat Karthik, J., Sharma, A., Lakshminarayan, A.: Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. Phys. Rev. A 75, 022304 (2007)CrossRefADS Karthik, J., Sharma, A., Lakshminarayan, A.: Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. Phys. Rev. A 75, 022304 (2007)CrossRefADS
22.
23.
Zurück zum Zitat Bose, S.: Quantum communication through spin chain dynamics: an introductory overview. Contemp. Phys. 48, 13–30 (2007)CrossRefADS Bose, S.: Quantum communication through spin chain dynamics: an introductory overview. Contemp. Phys. 48, 13–30 (2007)CrossRefADS
24.
Zurück zum Zitat Yang, S., Bayat, A., Bose, S.: Entanglement-enhanced information transfer through strongly correlated systems and its application to optical lattices. Phys. Rev. A 84, 020302(R) (2011)CrossRefADS Yang, S., Bayat, A., Bose, S.: Entanglement-enhanced information transfer through strongly correlated systems and its application to optical lattices. Phys. Rev. A 84, 020302(R) (2011)CrossRefADS
25.
Zurück zum Zitat Rafiee, M., Mokhtari, H.: Long-distance entanglement generation by local rotational protocols in spin chains. Phys. Rev. 87, 022304 (2013)CrossRefADS Rafiee, M., Mokhtari, H.: Long-distance entanglement generation by local rotational protocols in spin chains. Phys. Rev. 87, 022304 (2013)CrossRefADS
26.
Zurück zum Zitat Kontorovich, V.M., Tsukernik, V.M.: Magnetic properties of a spin array with two sublattices. Sov. Phys. JETP 26, 687–691 (1968)ADS Kontorovich, V.M., Tsukernik, V.M.: Magnetic properties of a spin array with two sublattices. Sov. Phys. JETP 26, 687–691 (1968)ADS
27.
Zurück zum Zitat Perk, J., Capel, H., Zuilhof, M., Siskens, T.J.: Magnetic properties of a spin array with two sublattices. Phys. A 81A, 319–348 (1975)CrossRefADS Perk, J., Capel, H., Zuilhof, M., Siskens, T.J.: Magnetic properties of a spin array with two sublattices. Phys. A 81A, 319–348 (1975)CrossRefADS
28.
Zurück zum Zitat Diederix, K., Groen, J.P., Poulis, N.: A study of the high field phase transition in Cu(NO3)2.2(1/2)H2O. Physica 86–88B, 1151–1152 (1977) Diederix, K., Groen, J.P., Poulis, N.: A study of the high field phase transition in Cu(NO3)2.2(1/2)H2O. Physica 86–88B, 1151–1152 (1977)
29.
Zurück zum Zitat Diederix, K.M., Groen, J.P., Henkens, L.S.J.M., Klaassen, T., Poulis, N.J.: An experimental study on the magnetic properties ground-state system in Cu(NO3)2.2-1/2H2O of the singlet. Physica 93B, 99–113 (1978) Diederix, K.M., Groen, J.P., Henkens, L.S.J.M., Klaassen, T., Poulis, N.J.: An experimental study on the magnetic properties ground-state system in Cu(NO3)2.2-1/2H2O of the singlet. Physica 93B, 99–113 (1978)
30.
Zurück zum Zitat Diederix, K.M., Groen, J.P., Henkens, L.S.J.M., Klaassen, T., Poulis, N.J.: An experimental study on the magnetic properties of the singlet ground-state system in CU(NO3)2.2-1/2H2O. Physica 94B, 9–26 (1978) Diederix, K.M., Groen, J.P., Henkens, L.S.J.M., Klaassen, T., Poulis, N.J.: An experimental study on the magnetic properties of the singlet ground-state system in CU(NO3)2.2-1/2H2O. Physica 94B, 9–26 (1978)
31.
Zurück zum Zitat Diederix, K.M., Blote, H.W.J., Groen, J.P., Klaassen, T.O., Poulis, N.: An experimental study on the magnetic properties of the singlet ground-state system in CU(NO3)2.2-1/2H2O. Phys. Rev. B 19, 420–431 (1979)CrossRefADS Diederix, K.M., Blote, H.W.J., Groen, J.P., Klaassen, T.O., Poulis, N.: An experimental study on the magnetic properties of the singlet ground-state system in CU(NO3)2.2-1/2H2O. Phys. Rev. B 19, 420–431 (1979)CrossRefADS
32.
Zurück zum Zitat Bonner, J.C., Fisher, M.E.: Linear magnetic chains with anisotroyic coupling. Phys. Rev. 135(3A), A640–A658 (1964)CrossRefADS Bonner, J.C., Fisher, M.E.: Linear magnetic chains with anisotroyic coupling. Phys. Rev. 135(3A), A640–A658 (1964)CrossRefADS
33.
Zurück zum Zitat Hida, K.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. Phys. Rev. B 45, 2207–2212 (1992)MathSciNetCrossRefADS Hida, K.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. Phys. Rev. B 45, 2207–2212 (1992)MathSciNetCrossRefADS
34.
Zurück zum Zitat Feldman, E.B., Rudavets, M.G.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. JETP Lett. 81, 47–52 (2005)CrossRefADS Feldman, E.B., Rudavets, M.G.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. JETP Lett. 81, 47–52 (2005)CrossRefADS
35.
Zurück zum Zitat Kuznetsova, E.I., Feldman, B.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. J. Exp. Theor. Phys. 102, 882–893 (2006)CrossRefADS Kuznetsova, E.I., Feldman, B.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. J. Exp. Theor. Phys. 102, 882–893 (2006)CrossRefADS
36.
Zurück zum Zitat Chitra, R., Pati, S., Krishnamurthy, H.R., Sen, D., Ramasesha, S.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. Phy. Rev. B 52, 6581–6587 (1995)CrossRefADS Chitra, R., Pati, S., Krishnamurthy, H.R., Sen, D., Ramasesha, S.: Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. Phy. Rev. B 52, 6581–6587 (1995)CrossRefADS
37.
Zurück zum Zitat Fledderjohann, A., Gros, C.: Spin dynamics of dimerized Heisenberg chains. Europhys. Lett. 37, 189–194 (1997)CrossRefADS Fledderjohann, A., Gros, C.: Spin dynamics of dimerized Heisenberg chains. Europhys. Lett. 37, 189–194 (1997)CrossRefADS
38.
Zurück zum Zitat Doronin, S.I., Pyrkov, A.N., Feldman, B.: Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian. JETP Lett. 85, 519–523 (2007)CrossRef Doronin, S.I., Pyrkov, A.N., Feldman, B.: Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian. JETP Lett. 85, 519–523 (2007)CrossRef
39.
Zurück zum Zitat Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Harcourt Asia Pvt. Ltd., Singapore (2001) Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Harcourt Asia Pvt. Ltd., Singapore (2001)
40.
Zurück zum Zitat Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)CrossRefADS Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)CrossRefADS
41.
Zurück zum Zitat Cheng, W., Shan, C., Sheng, Y., Gong, L., Zhao, S.: Quantum correlation approach to criticality in the XX spin chain with multiple interaction. Phys. B 407, 3671–3675 (2012)CrossRefADS Cheng, W., Shan, C., Sheng, Y., Gong, L., Zhao, S.: Quantum correlation approach to criticality in the XX spin chain with multiple interaction. Phys. B 407, 3671–3675 (2012)CrossRefADS
42.
Zurück zum Zitat Cheng, W.W., Du, Z.Z., Gong, L.Y., Zhao, S.M., Liu, J.M.: Signature of topological quantum phase transitions via Wigner-Yanase skew information. EPL 108, 46003 (2014)CrossRefADS Cheng, W.W., Du, Z.Z., Gong, L.Y., Zhao, S.M., Liu, J.M.: Signature of topological quantum phase transitions via Wigner-Yanase skew information. EPL 108, 46003 (2014)CrossRefADS
43.
Zurück zum Zitat Cheng, W.W., Li, J.X., Shan, C.J., Gong, L.Y., Zhao, S.M.: Criticality, factorization and Wigner-Yanase skew information in quantum spin chains. Quantum Inf. Process. 14, 2535–2549 (2015)CrossRefADS Cheng, W.W., Li, J.X., Shan, C.J., Gong, L.Y., Zhao, S.M.: Criticality, factorization and Wigner-Yanase skew information in quantum spin chains. Quantum Inf. Process. 14, 2535–2549 (2015)CrossRefADS
44.
Zurück zum Zitat Shan, C.J., Cheng, W.W., Liu, J.B., Cheng, Y.S.: Scaling of geometric quantum discord close to a topological phase transition. Sci. Rep. 4, 4473 (2014)CrossRefADS Shan, C.J., Cheng, W.W., Liu, J.B., Cheng, Y.S.: Scaling of geometric quantum discord close to a topological phase transition. Sci. Rep. 4, 4473 (2014)CrossRefADS
Metadaten
Titel
Quantum phase transition in dimerised spin-1/2 chains
verfasst von
Aparajita Das
Sreeparna Bhadra
Sonali Saha
Publikationsdatum
01.11.2015
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 11/2015
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-015-1116-8

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