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Volumn 324, Issue 5, 2009, Pages 977-1057

A symmetry principle for topological quantum order

Author keywords

Entanglement entropy; Gauge theories; String and non local correlators; Symmetries; Thermal fragility; Topological quantum order

Indexed keywords


EID: 62849094297     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2008.11.002     Document Type: Article
Times cited : (351)

References (122)
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    • Z. Nussinov, G. Ortiz, cond-mat/0702377.
    • Z. Nussinov, G. Ortiz, cond-mat/0702377.
  • 4
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    • Z. Nussinov, G. Ortiz, cond-mat/0605316.
    • Z. Nussinov, G. Ortiz, cond-mat/0605316.
  • 10
    • 62849116652 scopus 로고    scopus 로고
    • note
    • topo = 1.
  • 17
    • 62849088988 scopus 로고    scopus 로고
    • M. Oshikawa, Y.-B. Kim, K. Shtengel, C. Nayak, S. Tewari, cond-mat/0607743.
    • M. Oshikawa, Y.-B. Kim, K. Shtengel, C. Nayak, S. Tewari, cond-mat/0607743.
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    • cond-mat/0606075
    • Z. Nussinov, cond-mat/0606075.
    • Nussinov, Z.1
  • 57
    • 62849118256 scopus 로고    scopus 로고
    • note
    • β 〉 are eigenstates of H with the same eigenvalue.
  • 61
    • 62849106238 scopus 로고    scopus 로고
    • note
    • max and states which differ by a finite number of spin flips is algebraically small in the system size. The general matrix element of a quasi-local operator between different (orthogonal) symmetry eigenstates can be computed by the Clebsch-Gordan coefficients and is seen to be exponentially small in the system size.
  • 64
    • 35848938732 scopus 로고    scopus 로고
    • Some time after we found the mappings to the Ising chain [3, 4], we learned that H. Chen and J. Hu later arrived independently, by fermionization, at a similar conclusion regarding the equivalence of this model to an Ising chain:
    • Some time after we found the mappings to the Ising chain [3, 4], we learned that H. Chen and J. Hu later arrived independently, by fermionization, at a similar conclusion regarding the equivalence of this model to an Ising chain:. Chen H.-D., and Hu J. Phys. Rev. B 76 (2007) 193101
    • (2007) Phys. Rev. B , vol.76 , pp. 193101
    • Chen, H.-D.1    Hu, J.2
  • 67
    • 62849105808 scopus 로고    scopus 로고
    • note
    • {norm of matrix} P {norm of matrix}. From these relations, Eq. (111) follows.
  • 68
    • 62849115898 scopus 로고    scopus 로고
    • note
    • s) needs to be much larger than the separation of the spins {norm of matrix} R {norm of matrix}.
  • 69
    • 62849108369 scopus 로고    scopus 로고
    • note
    • i → c with a finite non-zero (nor infinite c).
  • 76
    • 62849098936 scopus 로고    scopus 로고
    • H. Katsura, T. Hirano, Y. Hatsugai, cond-mat/0702196.
    • H. Katsura, T. Hirano, Y. Hatsugai, cond-mat/0702196.
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    • 62849123483 scopus 로고    scopus 로고
    • note
    • D - 1) scaling although no TQO might exist in this system of tight binding fermions.
  • 97
    • 62849087748 scopus 로고    scopus 로고
    • F. Anfuso, A. Rosch, cond-mat/0609051, cond-mat/0702064.
    • F. Anfuso, A. Rosch, cond-mat/0609051, cond-mat/0702064.
  • 100
    • 62849116886 scopus 로고    scopus 로고
    • note
    • Ns + 2 g - 1.
  • 101
    • 62849108368 scopus 로고    scopus 로고
    • note
    • p = 1 with R a region which does not span the entire lattice.
  • 102
    • 62849124276 scopus 로고    scopus 로고
    • note
    • - 3 / 2 .
  • 122
    • 62849107169 scopus 로고    scopus 로고
    • Z. Nussinov, G. Ortiz, arXiv:0812.4309 (2008).
    • Z. Nussinov, G. Ortiz, arXiv:0812.4309 (2008).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.