메뉴 건너뛰기




Volumn 77, Issue 1, 2008, Pages

Scaling properties of fidelity in the spin-1 anisotropic model

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; NUMERICAL ANALYSIS; PHASE TRANSITIONS; QUANTUM THEORY;

EID: 40749119784     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.012311     Document Type: Article
Times cited : (118)

References (47)
  • 5
    • 37649027994 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203
    • H. Fan, V. Korepin, and V. Roychowdhury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203 93, 227203 (2004).
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 227203
    • Fan, H.1    Korepin, V.2    Roychowdhury, V.3
  • 6
    • 34447101731 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.76.012401
    • H. Katsura, T. Hirano, and Y. Hatsugai, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.012401 76, 012401 (2007).
    • (2007) Phys. Rev. B , vol.76 , pp. 012401
    • Katsura, H.1    Hirano, T.2    Hatsugai, Y.3
  • 8
    • 2442674839 scopus 로고
    • NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2
    • C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2 424, 443 (1994).
    • (1994) Nucl. Phys. B , vol.424 , pp. 443
    • Holzhey, C.1    Larsen, F.2    Wilczek, F.3
  • 9
    • 2442560099 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.92.096402
    • V. E. Korepin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 096402 92, 096402 (2004).
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 096402
    • Korepin, V.E.1
  • 13
    • 40749141043 scopus 로고    scopus 로고
    • arXiv:0708.2978.
    • For a recent review, see J. Cardy, e-print arXiv:0708.2978.
    • Cardy, J.1
  • 15
    • 33749345011 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.74.031123
    • P. Zanardi and N. Paunković, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.031123 74, 031123 (2006).
    • (2006) Phys. Rev. e , vol.74 , pp. 031123
    • Zanardi, P.1    Paunković, N.2
  • 16
    • 34547869745 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.76.022101
    • W. L. You, Y. W. Li, and S. J. Gu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.022101 76, 022101 (2007).
    • (2007) Phys. Rev. e , vol.76 , pp. 022101
    • You, W.L.1    Li, Y.W.2    Gu, S.J.3
  • 18
    • 33846604250 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.75.014439
    • M. Cozzini, P. Giorda, and P. Zanardi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.014439 75, 014439 (2007).
    • (2007) Phys. Rev. B , vol.75 , pp. 014439
    • Cozzini, M.1    Giorda, P.2    Zanardi, P.3
  • 19
    • 34648814053 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.76.104420
    • M. Cozzini, R. Ionicioiu, and P. Zanardi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.104420 76, 104420 (2007).
    • (2007) Phys. Rev. B , vol.76 , pp. 104420
    • Cozzini, M.1    Ionicioiu, R.2    Zanardi, P.3
  • 20
    • 33947256773 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.98.110601
    • P. Buonsante and A. Vezzani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.110601 98, 110601 (2007).
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 110601
    • Buonsante, P.1    Vezzani, A.2
  • 21
    • 33947301917 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.75.115119
    • N. Oelkers and J. Links, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.115119 75, 115119 (2007).
    • (2007) Phys. Rev. B , vol.75 , pp. 115119
    • Oelkers, N.1    Links, J.2
  • 22
    • 34548549064 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.99.100603
    • P. Zanardi, P. Giorda, and M. Cozzini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.100603 99, 100603 (2007).
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 100603
    • Zanardi, P.1    Giorda, P.2    Cozzini, M.3
  • 23
    • 34548454416 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.99.095701
    • L. Campos Venuti and P. Zanardi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.095701 99, 095701 (2007).
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 095701
    • Campos Venuti, L.1    Zanardi, P.2
  • 25
    • 37049015409 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.76.061108
    • S. Chen, L. Wang, S. J. Gu, and Y. Wang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.061108 76, 061108 (2007).
    • (2007) Phys. Rev. e , vol.76 , pp. 061108
    • Chen, S.1    Wang, L.2    Gu, S.J.3    Wang, Y.4
  • 28
    • 40749148407 scopus 로고    scopus 로고
    • arXiv:0704.2945.
    • H. Q. Zhou, e-print arXiv:0704.2945.
    • Zhou, H.Q.1
  • 29
    • 36049013005 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.76.180403
    • M. F. Yang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.180403 76, 180403 (R) (2007).
    • (2007) Phys. Rev. B , vol.76 , pp. 180403
    • Yang, M.F.1
  • 30
    • 3442895828 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.69.2863
    • S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69. 2863 69, 2863 (1992);
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2863
    • White, S.R.1
  • 31
    • 20044389808 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.48.10345
    • S. R. White, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.10345 48, 10345 (1993);
    • (1993) Phys. Rev. B , vol.48 , pp. 10345
    • White, S.R.1
  • 32
    • 23844520141 scopus 로고    scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.77.259
    • U. Schollwöck, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 77.259 77, 259 (2005).
    • (2005) Rev. Mod. Phys. , vol.77 , pp. 259
    • Schollwöck, U.1
  • 33
    • 35949018843 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.34.6372
    • H. J. Schulz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.6372 34, 6372 (1986).
    • (1986) Phys. Rev. B , vol.34 , pp. 6372
    • Schulz, H.J.1
  • 34
    • 7244220861 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.40.4709
    • M. den Nijs and K. Rommelse, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.4709 40, 4709 (1989).
    • (1989) Phys. Rev. B , vol.40 , pp. 4709
    • Den Nijs, M.1    Rommelse, K.2
  • 35
    • 0038756041 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.67.104401
    • W. Chen, K. Hida, and B. C. Sanctuary, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.104401 67, 104401 (2003).
    • (2003) Phys. Rev. B , vol.67 , pp. 104401
    • Chen, W.1    Hida, K.2    Sanctuary, B.C.3
  • 38
    • 40749091147 scopus 로고    scopus 로고
    • Here we use the notations of Ref..
    • Here we use the notations of Ref..
  • 39
    • 0031548107 scopus 로고    scopus 로고
    • NUPBBO 0550-3213 10.1016/S0550-3213(97)00123-5
    • S. Lukyanov and A. Zamolodchikov, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(97)00123-5 493, 571 (1997).
    • (1997) Nucl. Phys. B , vol.493 , pp. 571
    • Lukyanov, S.1    Zamolodchikov, A.2
  • 40
    • 40749158617 scopus 로고    scopus 로고
    • To lift the double degeneracy in the Néel phase, a Zeeman term h1 S1z acting only upon the spin at site 1 is added in the Hamiltonian of Eq. 2. Here we take the boundary magnetic field h1 =-0.01. The inclusion of this tiny Zeeman splitting selects a specific ground state and stabilizes our calculations of the fidelity in the Néel phase. Nevertheless, this term is found to have no significant effect on the entanglement entropy and the fidelity in other phases.
    • To lift the double degeneracy in the Néel phase, a Zeeman term h1 S1z acting only upon the spin at site 1 is added in the Hamiltonian of Eq. 2. Here we take the boundary magnetic field h1 =-0.01. The inclusion of this tiny Zeeman splitting selects a specific ground state and stabilizes our calculations of the fidelity in the Néel phase. Nevertheless, this term is found to have no significant effect on the entanglement entropy and the fidelity in other phases.
  • 41
    • 40749106467 scopus 로고    scopus 로고
    • The DMRG method had been used to calculate the overlap of two different ground states for a decade. For example, people had applied this technique to evaluate the exponent of the orthogonality catastrophe for the problem of a single impurity in a one-dimensional Luttinger liquid.
    • The DMRG method had been used to calculate the overlap of two different ground states for a decade. For example, people had applied this technique to evaluate the exponent of the orthogonality catastrophe for the problem of a single impurity in a one-dimensional Luttinger liquid.
  • 42
    • 0001234057 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.54.R9643
    • S. Qin, M. Fabrizio, and L. Yu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.R9643 54, R9643 (1996);
    • (1996) Phys. Rev. B , vol.54 , pp. 9643
    • Qin, S.1    Fabrizio, M.2    Yu, L.3
  • 44
    • 35948966063 scopus 로고    scopus 로고
    • For a recent review, see ZZZZZZ 1742-5468
    • For a recent review, see I. P. McCulloch, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 2007, P10014.
    • J. Stat. Mech.: Theory Exp. , vol.2007 , pp. 10014
    • McCulloch, I.P.1
  • 45
    • 0001574528 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.28.1516
    • M. E. Fisher and M. N. Barber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28.1516 28, 1516 (1972);
    • (1972) Phys. Rev. Lett. , vol.28 , pp. 1516
    • Fisher, M.E.1    Barber, M.N.2
  • 46
    • 0001315226 scopus 로고
    • edited by C. Domb and J. L. Lebowitz (Academic Press, London
    • M. N. Barber, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic Press, London, 1983), Vol. 8, p. 145.
    • (1983) Phase Transitions and Critical Phenomena , vol.8 , pp. 145
    • Barber, M.N.1
  • 47
    • 40749118797 scopus 로고    scopus 로고
    • We note that the DMRG calculations in Refs. and are under the periodic boundary conditions, rather than the open boundary conditions used in the present work. The small discrepancy of our results from theirs may be due to the different boundary conditions employed.
    • We note that the DMRG calculations in Refs. and are under the periodic boundary conditions, rather than the open boundary conditions used in the present work. The small discrepancy of our results from theirs may be due to the different boundary conditions employed.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.