메뉴 건너뛰기




Volumn 80, Issue 1, 2009, Pages

Singularities in ground-state fidelity and quantum phase transitions for the Kitaev model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 68949104336     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.014403     Document Type: Article
Times cited : (68)

References (51)
  • 3
    • 68949156987 scopus 로고    scopus 로고
    • arXiv:cond-mat/0702377 (unpublished).
    • Z. Nussinov and G. Ortiz, arXiv:cond-mat/0702377 (unpublished).
    • Nussinov, Z.1    Ortiz, G.2
  • 4
    • 68949164482 scopus 로고    scopus 로고
    • However, the existence of a mapping from a system with topological order to a system with symmetry-breaking order is possible, as shown for the Kitaev model (Ref.).
    • However, the existence of a mapping from a system with topological order to a system with symmetry-breaking order is possible, as shown for the Kitaev model (Ref.).
  • 5
    • 30444456387 scopus 로고    scopus 로고
    • 10.1016/j.aop.2005.10.005
    • A. Kitaev, Ann. Phys. 321, 2 (2006). 10.1016/j.aop.2005.10.005
    • (2006) Ann. Phys. , vol.321 , pp. 2
    • Kitaev, A.1
  • 6
    • 0037268624 scopus 로고    scopus 로고
    • 10.1016/S0003-4916(02)00018-0
    • A. Yu. Kitaev, Ann. Phys. 303, 2 (2003). 10.1016/S0003-4916(02)00018-0
    • (2003) Ann. Phys. , vol.303 , pp. 2
    • Yu. Kitaev, A.1
  • 17
    • 68949156988 scopus 로고    scopus 로고
    • arXiv:0704.2945 (unpublished).
    • H.-Q. Zhou, arXiv:0704.2945 (unpublished).
    • Zhou, H.-Q.1
  • 20
    • 68949141411 scopus 로고    scopus 로고
    • arXiv:0803.0585 (unpublished).
    • H.-Q. Zhou, arXiv:0803.0585 (unpublished).
    • Zhou, H.-Q.1
  • 21
    • 68949152496 scopus 로고    scopus 로고
    • It is a difficult task to evaluate the ground state fidelity per site if a quantum lattice system is not exactly solvable. However, thanks to the latest advances in classical simulations of quantum lattice systems (Refs.), a practical way to compute it is now available using the tensor network algorithms for translationally invariant infinite-size quantum lattice systems (Ref.).
    • It is a difficult task to evaluate the ground state fidelity per site if a quantum lattice system is not exactly solvable. However, thanks to the latest advances in classical simulations of quantum lattice systems (Refs.), a practical way to compute it is now available using the tensor network algorithms for translationally invariant infinite-size quantum lattice systems (Ref.).
  • 22
    • 68949152497 scopus 로고    scopus 로고
    • arXiv:cond-mat/0611167 (unpublished).
    • R. J. Baxter, arXiv:cond-mat/0611167 (unpublished).
    • Baxter, R.J.1
  • 23
    • 33749345011 scopus 로고    scopus 로고
    • Another fidelity approach to QPTs is based on the fidelity between two neighboring states, see 10.1103/PhysRevE.74.031123;
    • Another fidelity approach to QPTs is based on the fidelity between two neighboring states, see P. Zanardi and N. Paunković, Phys. Rev. E 74, 031123 (2006) 10.1103/PhysRevE.74.031123
    • (2006) Phys. Rev. e , vol.74 , pp. 031123
    • Zanardi, P.1    Paunković, N.2
  • 25
    • 33947301917 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.75.115119;
    • N. Oelkers and J. Links, Phys. Rev. B 75, 115119 (2007) 10.1103/PhysRevB.75.115119
    • (2007) Phys. Rev. B , vol.75 , pp. 115119
    • Oelkers, N.1    Links, J.2
  • 28
    • 33947256773 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.98.110601;
    • P. Buonsante and A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007) 10.1103/PhysRevLett.98.110601
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 110601
    • Buonsante, P.1    Vezzani, A.2
  • 29
    • 34547869745 scopus 로고    scopus 로고
    • 10.1103/PhysRevE.76.022101;
    • W.-L. You, Y.-W. Li, and S.-J. Gu, Phys. Rev. E 76, 022101 (2007) 10.1103/PhysRevE.76.022101
    • (2007) Phys. Rev. e , vol.76 , pp. 022101
    • You, W.-L.1    Li, Y.-W.2    Gu, S.-J.3
  • 32
    • 40749119784 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.77.012311;
    • Y. C. Tzeng and M. F. Yang, Phys. Rev. A 77, 012311 (2008) 10.1103/PhysRevA.77.012311
    • (2008) Phys. Rev. A , vol.77 , pp. 012311
    • Tzeng, Y.C.1    Yang, M.F.2
  • 35
    • 36049013005 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.76.180403;
    • M. F. Yang, Phys. Rev. B 76, 180403 (R) (2007) 10.1103/PhysRevB.76.180403
    • (2007) Phys. Rev. B , vol.76 , pp. 180403
    • Yang, M.F.1
  • 36
    • 51349105885 scopus 로고    scopus 로고
    • 10.1088/1742-5468/2008/07/P07011
    • J. O. Fjaerestad, J. Stat. Mech. 2008, P07011 (2008). 10.1088/1742-5468/2008/07/P07011
    • (2008) J. Stat. Mech. , vol.2008 , pp. 07011
    • Fjaerestad, J.O.1
  • 37
    • 68949150499 scopus 로고    scopus 로고
    • arXiv:cond-mat/0703633 (unpublished).
    • H.-D. Chen and Z. Nussinov, arXiv:cond-mat/0703633 (unpublished).
    • Chen, H.-D.1    Nussinov, Z.2
  • 38
  • 40
    • 35848938732 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.76.193101
    • H.-D. Chen and J. P. Hu, Phys. Rev. B 76, 193101 (2007). 10.1103/PhysRevB.76.193101
    • (2007) Phys. Rev. B , vol.76 , pp. 193101
    • Chen, H.-D.1    Hu, J.P.2
  • 42
    • 33846978099 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.98.070201
    • G. Vidal, Phys. Rev. Lett. 98, 070201 (2007). 10.1103/PhysRevLett.98. 070201
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 070201
    • Vidal, G.1
  • 44
    • 52149091646 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.101.110501
    • G. Vidal, Phys. Rev. Lett. 101, 110501 (2008). 10.1103/PhysRevLett.101. 110501
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 110501
    • Vidal, G.1
  • 45
    • 36549074539 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.99.220405;
    • G. Vidal, Phys. Rev. Lett. 99, 220405 (2007) 10.1103/PhysRevLett.99. 220405
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 220405
    • Vidal, G.1
  • 46
    • 65549170919 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.79.144108;
    • G. Evenbly and G. Vidal, Phys. Rev. B 79, 144108 (2009) 10.1103/PhysRevB.79.144108
    • (2009) Phys. Rev. B , vol.79 , pp. 144108
    • Evenbly, G.1    Vidal, G.2
  • 48
    • 68949152491 scopus 로고    scopus 로고
    • This amounts to the statement that the fidelity per lattice site does not depend on which state has been chosen among degenerate states in the ground state subspace for a system with topological order. This has been shown for different states of the toric code (Ref.). That is, the tensor network representation for different states shares the same tensors except for their top tensor, where the relevant topological information is stored. Such a difference does not contribute to the fidelity per lattice site.
    • This amounts to the statement that the fidelity per lattice site does not depend on which state has been chosen among degenerate states in the ground state subspace for a system with topological order. This has been shown for different states of the toric code (Ref.). That is, the tensor network representation for different states shares the same tensors except for their top tensor, where the relevant topological information is stored. Such a difference does not contribute to the fidelity per lattice site.
  • 49
    • 68949155085 scopus 로고    scopus 로고
    • For generic Jx, Jy, and Jz, we have k1 =1/ (8 π2 Jx Jy).
    • For generic Jx, Jy, and Jz, we have k1 =1/ (8 π2 Jx Jy).
  • 50
    • 0003480237 scopus 로고
    • edited by C. Domb and J. L. Lebowitz (Academic, London
    • M. N. Barber, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic, London, 1983), Vol. 8.
    • (1983) Phase Transitions and Critical Phenomena , vol.8
    • Barber, M.N.1
  • 51
    • 40849088480 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.100.070404
    • M. Aguado and G. Vidal, Phys. Rev. Lett. 100, 070404 (2008). 10.1103/PhysRevLett.100.070404
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 070404
    • Aguado, M.1    Vidal, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.