Abstract
The modified spin-wave (MSW) theory and SU(N) Schwinger boson theory (SBW) are employed to study the quantum entanglement in one- (1D) and two-dimensional (2D) Heisenberg antiferromagnets with Dzyaloshinskii–Moriya (DM) interaction which are models to superconducting materials of high critical temperature Tc such as La2CuO4. For the 1D case, we consider integer spin and for 2D case, since the behavior is independent on the spin value, we consider the one-half-spin and square lattice. We get the entanglement entropy in function of the temperature T where we have not gotten large variation of the quantum entanglement with the changing of the anisotropy Δ and DM interaction constant D.
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D.J. Scalapino, in Handbook of High-Temperature Superconductivity, edited by J.R. Schrieffer, J.S. Brooks (Springer, New York, 2007)
S. Sachdev, Science 336, 1510 (2012)
L.S. Lima, Solid State Commun. 258, 21 (2017)
L.S. Lima, Physica C 527, 33 (2016)
F. Iemini, T.O. Maciel, R.O. Vianna, Phys. Rev. B 92, 075423 (2015)
F. Iemini, L. da Silva Souza, T. Debarba, A.T. Cesario, T.O. Maciel, R.O. Vianna, Eur. Phys. J. D 71, 119 (2017)
K.H. Norwich, Physica A 462, 141 (2016)
L.S. Lima, J. Mod. Phys. 06, 2231 (2015)
L.S. Lima, Physica A 483, 239 (2017)
L.S. Lima, Physica A 492, 1853 (2018)
N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)
F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)
F.D.M. Haldane, Phys. Lett. A 93, 464 (1983)
E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961)
E.H. Lieb, D. Mattis, J. Math. Phys. 3, 749 (1962)
L.S. Lima, A.S.T. Pires, J. Magn. Magn. Mater. 322, 2157 (2010)
A.R. Pereira, S.A. Leonel, P.Z. Coura, B.V. Costa, Phys. Rev. B 71, 014403 (2005)
T. Roscilde, S. Haas, Phys. Rev. Lett. 99, 047205 (2007)
L.S. Lima, A.S.T. Pires, B.V. Costa, Physica A 438, 579 (2015)
L.S. Lima, A.S.T. Pires, B.V. Costa, J. Magn. Magn. Mater. 371, 89 (2014)
A.S.T. Pires, L.S. Lima, Phys. Rev. B 79, 064401 (2009)
A. Einstein, E. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)
A. Metavitsiadis, D. Sellmann, S. Eggert, Phys. Rev. B, 89, 241104 (2014)
A.L. de Paula, J.G.G. de Oliveira, J.G. Peixoto de Faria, D.S. Freitas, M.C. Nemes, Phys. Rev. A 89, 022303 (2014)
A.F. Kracklauer, J. Mod. Phys. 6, 1961 (2015)
G. Vidal, J.L. Latorre, E.I. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
A.L. Malvezzi, G. Karpat, B. Cakmak, F.F. Fanchini, T. Debarba, R.O. Vianna, Phys. Rev. B 93, 184428 (2016)
T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)
A.R. Its, B.-Q. Jin, V.E. Korepin, J. Phys. A: Math. Gen. 38, 2975 (2005)
J.I. Latorre, E. Rico, G. Vidal, Quant. Inf. Comput. 4, 48 (2004)
S. Sachdev, Quantum Phase Transitions, 2nd edn. (Cambridge, UK, 2011)
D. Bruss, G. Leuchs, Lectures on Quantum Information (WLEY-VCH Verlag, Weinheim, Germany, 2007)
E. Fradkin, Field Theories of Condensed Matter Physics, 2nd edn. (Cambridge, UK, 2013)
P. Calabrense, J. Cardy, J. Stat. Mech.: Theory Exp. 2004, P06002 (2004)
D. Bianchini, O.A. Castro-Alvaredo, B. Doyon, E. Levi, F. Ravanini, J. Phys. A: Math. Theor. 48, 04FT01 (2015)
A.S.T. Pires, M.E. Gouvea, J. Magn. Magn. Mater. 241, 31 (2002)
L.S. Lima, A.S.T. Pires, J. Phys.: Condens. Matter 19, 436218 (2007)
L.S. Lima, Eur. Phys. J. B 93, 99 (2013)
L.S. Lima, Physica B 437, 28 (2014)
M. Takahashi, Phys. Rev. B 40, 2494 (1989)
D.P. Arovas, A. Auerbach, Phys. Rev. B 38, 316 (1988)
A. Auerbarch, Interacting Electrons and Quantum Magnetism (Springer, New York, 1994)
I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958)
T. Moriya, Phys. Rev. 120, 91 (1960)
I. Affleck, M. Oshikawa, Phys. Rev. B 60, 1038 (1999)
M. Oshikawa, I. Affleck, Phys. Rev. Lett. 79, 2883 (1997)
I. Garate, I. Affleck, Phys. Rev. B 81, 144419 (2010)
L.S. Lima, Phys. Status Solidi B 249, 1613 (2012)
L.S. Lima, A.S.T. Pires, J. Magn. Magn. Mater. 320, 2316 (2008)
L.S. Lima, Physica C 549, 147 (2018)
L.S. Lima, J. Magn. Magn. Mater. 454, 150 (2018)
U. Schotte, A. Kelnberger, N. Stusser, J. Phys.: Condens. Matter 10, 6391 (1998)
A.E. Jacobs, T. Nikuni, J. Phys.: Condens. Matter 10, 6405 (1998)
D.N. Aristov, S.V. Maleyev, Phys. Rev. B 62, R751 (2000)
C.J. De Leone, G.T. Zimanyi, Phys. Rev. B 49, 1131 (1994)
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Lima, L.S. Effect of Dzyaloshinskii–Moriya interaction on quantum entanglement in superconductors models of high Tc. Eur. Phys. J. D 73, 6 (2019). https://doi.org/10.1140/epjd/e2018-90439-5
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DOI: https://doi.org/10.1140/epjd/e2018-90439-5