메뉴 건너뛰기




Volumn 77, Issue 3, 2008, Pages

Analytic results on long-distance entanglement mediated by gapped spin chains

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETISM; COMPUTATION THEORY; CORRELATION METHODS; SPIN DYNAMICS; THERMODYNAMICS;

EID: 40849139265     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.034301     Document Type: Article
Times cited : (16)

References (33)
  • 3
    • 1642587733 scopus 로고    scopus 로고
    • QICUAW 1533-7146 10.1103/PhysRevLett.90.227902
    • J. I. Latorre, E. Rico, and G. Vidal, Quantum Inf. Comput. QICUAW 1533-7146 10.1103/PhysRevLett.90.227902 4, 48 (2004).
    • (2004) Quantum Inf. Comput. , vol.4 , pp. 48
    • Latorre, J.I.1    Rico, E.2    Vidal, G.3
  • 4
    • 0036757880 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.66.032110
    • T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002)
    • (2002) Phys. Rev. A , vol.66 , pp. 032110
    • Osborne, T.J.1    Nielsen, M.A.2
  • 7
    • 4644244245 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/6/1/102
    • V. Vedral, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/6/1/102 6, 102 (2004).
    • (2004) New J. Phys. , vol.6 , pp. 102
    • Vedral, V.1
  • 8
    • 33745054887 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/8/6/095
    • G. De Chiara, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/6/095 8, 95 (2006).
    • (2006) New J. Phys. , vol.8 , pp. 95
    • De Chiara, G.1
  • 9
    • 23344438573 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/7/1/073
    • M. B. Plenio and F. L. Semião, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/073 7, 73 (2005)
    • (2005) New J. Phys. , vol.7 , pp. 73
    • Plenio, M.B.1    Semião, F.L.2
  • 13
    • 0346688149 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.61.052306
    • V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052306 61, 052306 (2000).
    • (2000) Phys. Rev. A , vol.61 , pp. 052306
    • Coffman, V.1    Kundu, J.2    Wootters, W.K.3
  • 14
    • 0036509287 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.65.032314
    • G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002).
    • (2002) Phys. Rev. A , vol.65 , pp. 032314
    • Vidal, G.1    Werner, R.F.2
  • 15
    • 18144365928 scopus 로고
    • PHRVAO 0031-899X 10.1103/PhysRev.149.491
    • J. R. Schrieffer and P. A. Wolff, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.149.491 149, 491 (1966).
    • (1966) Phys. Rev. , vol.149 , pp. 491
    • Schrieffer, J.R.1    Wolff, P.A.2
  • 16
    • 40849085974 scopus 로고    scopus 로고
    • P0 H0 P0 contributes with a constant, and thus will be set to zero as it does not change the eigenstates.
    • P0 H0 P0 contributes with a constant, and thus will be set to zero as it does not change the eigenstates.
  • 17
    • 0002238950 scopus 로고
    • PTPKAV 0033-068X 10.1143/PTP.16.45
    • T. Kasuya, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.16.45 16, 45 (1956)
    • (1956) Prog. Theor. Phys. , vol.16 , pp. 45
    • Kasuya, T.1
  • 18
    • 0002105003 scopus 로고
    • PTPKAV 0033-068X 10.1143/PTP.16.58
    • T. Kasuya, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.16.58 16, 58 (1956)
    • (1956) Prog. Theor. Phys. , vol.16 , pp. 58
    • Kasuya, T.1
  • 19
    • 36149011918 scopus 로고
    • PHRVAO 0031-899X 10.1103/PhysRev.96.99
    • M. A. Ruderman and C. Kittel, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.96.99 96, 99 (1954)
    • (1954) Phys. Rev. , vol.96 , pp. 99
    • Ruderman, M.A.1    Kittel, C.2
  • 20
    • 34249913377 scopus 로고
    • PHRVAO 0031-899X 10.1103/PhysRev.106.893
    • K. Yosida, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.106.893 106, 893 (1957).
    • (1957) Phys. Rev. , vol.106 , pp. 893
    • Yosida, K.1
  • 21
    • 33344477235 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.71.022301
    • Y. Li, T. Shi, B. Chen, Z. Song, and C.-P. Sun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022301 71, 022301 (2005).
    • (2005) Phys. Rev. A , vol.71 , pp. 022301
    • Li, Y.1    Shi, T.2    Chen, B.3    Song, Z.4    Sun, C.-P.5
  • 22
    • 40849118968 scopus 로고    scopus 로고
    • We rewrite Hab as H (ab) =- - + dE E k>0 ψ0 | U Pk U | ψ0 δ (E- Ek + E0) and use the integral representation of the Dirac delta function δ (E) = (2π) -1 - + dt eiEt, and the fact that ψ0 | ei E0 t U ei Ek t Pk U | ψ0 = ψ0 | U (t) Pk U | ψ0, where U (t) = ei H0 t U e-i H0 t is the probe-spin-chain coupling in the Heisenberg representation for the spin chain. Finally we can set U 0 =0 to our advantage, by including the term k=0 in the sum over k and, since 1=k Pk, we obtain the stated result.
    • We rewrite Hab as H (ab) =- - + dE E k>0 ψ0 | U Pk U | ψ0 δ (E- Ek + E0) and use the integral representation of the Dirac delta function δ (E) = (2π) -1 - + dt eiEt, and the fact that ψ0 | ei E0 t U ei Ek t Pk U | ψ0 = ψ0 | U (t) Pk U | ψ0, where U (t) = ei H0 t U e-i H0 t is the probe-spin-chain coupling in the Heisenberg representation for the spin chain. Finally we can set U 0 =0 to our advantage, by including the term k=0 in the sum over k and, since 1=k Pk, we obtain the stated result.
  • 23
    • 40849088684 scopus 로고    scopus 로고
    • The local terms in H (ab) read HL (ab) = α,β=1 p (γαa aβa Cmα,mβ Aα Aβ 1b + γαb γβb Cnα,nβ 1a Bα Bβ) and HL a (b) = α=1 p γα a (b) A (B) α Omα. These terms are either constants or zero in the cases we consider.
    • The local terms in H (ab) read HL (ab) = α,β=1 p (γαa aβa Cmα,mβ Aα Aβ 1b + γαb γβb Cnα,nβ 1a Bα Bβ) and HL a (b) = α=1 p γα a (b) A (B) α Omα. These terms are either constants or zero in the cases we consider.
  • 24
    • 40849087055 scopus 로고    scopus 로고
    • More precisely, due to the perturbative nature of our formalism with expansion parameter Jp /Δ, the negativity or any other entanglement monotone will deviate from the value of maximal entanglement (the singlet state) with corrections of the order of (Jp /Δ) 2, which are negligible for weakly interacting probes, i.e., E (ρab) =1-O (Jp2 / Δ2).
    • More precisely, due to the perturbative nature of our formalism with expansion parameter Jp /Δ, the negativity or any other entanglement monotone will deviate from the value of maximal entanglement (the singlet state) with corrections of the order of (Jp /Δ) 2, which are negligible for weakly interacting probes, i.e., E (ρab) =1-O (Jp2 / Δ2).
  • 27
    • 40849087057 scopus 로고    scopus 로고
    • In a conformally invariant two-dimensional system with scaling dimension η the two-point correlation function has the transformation law G g′ (w1, w2) = | dw (z1) /d z1 dw (z2) /d z2 | -(η/2) Gg (z1, z2) generated by any analytic function w (z). The subscripts g and g′ refer to the boundary geometry where the theory is defined.
    • In a conformally invariant two-dimensional system with scaling dimension η the two-point correlation function has the transformation law G g′ (w1, w2) = | dw (z1) /d z1 dw (z2) /d z2 | -(η/2) Gg (z1, z2) generated by any analytic function w (z). The subscripts g and g′ refer to the boundary geometry where the theory is defined.
  • 28
    • 0000977044 scopus 로고
    • JPHAC5 0305-4470 10.1088/0305-4470/17/7/003
    • J. L. Cardy, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/7/003 17, L385 (1984).
    • (1984) J. Phys. A , vol.17 , pp. 385
    • Cardy, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.