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Volumn 318, Issue 2, 2005, Pages 316-344

From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the "Stochastic Matrix Form" decomposition

Author keywords

Loop models; Master equation; Quantum dimers; Rokhsar Kivelson Hamiltonians; Transition matrix

Indexed keywords


EID: 20844451423     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2005.01.006     Document Type: Article
Times cited : (152)

References (52)
  • 9
    • 20844447168 scopus 로고    scopus 로고
    • Available from:
    • R. Kenyon. Available from:
    • Kenyon, R.1
  • 34
    • 20844437267 scopus 로고    scopus 로고
    • The assumption that the Hilbert space is fully connected under the action of the time-evolution operator implies that the Hamiltonian matrix in the Hilbert space basis is irreducible. This requires in turn that no row or column in the matrix has less than non-vanishing off-diagonal element. Since the Hamiltonian is symmetric, we immediately obtain a lower bound for L , namely L ≥ 2( L - 1), and Eq. (3a) holds
    • The assumption that the Hilbert space is fully connected under the action of the time-evolution operator implies that the Hamiltonian matrix in the Hilbert space basis is irreducible. This requires in turn that no row or column in the matrix has less than non-vanishing off-diagonal element. Since the Hamiltonian is symmetric, we immediately obtain a lower bound for L , namely L ≥ 2( L - 1), and Eq. (3a) holds
  • 35
    • 20844438506 scopus 로고    scopus 로고
    • See Chapter 5 from Matrices: Theory and Applications, by D. Serre,Springer, New York, 2002. See also Chapter A4.1 from Quantum Field Theory and Critical Phenomena, by J.Zinn-Justin,Oxford University Press New York
    • See Chapter 5 from Matrices: Theory and Applications, by D. Serre,Springer, New York, 2002.
    • (2002)
  • 36
    • 20844461333 scopus 로고    scopus 로고
    • See also Chapter A4.1 from Quantum Field Theory and Critical Phenomena, by J.Zinn-Justin,Oxford University Press, New York
    • See also Chapter A4.1 from Quantum Field Theory and Critical Phenomena, by J.Zinn-Justin,Oxford University Press,New York, 1996.
    • (1996)
  • 37
    • 20844434500 scopus 로고    scopus 로고
    • +K(EC′-EC)/2)
    • +K(EC′-EC)/2).
  • 39
    • 20844454361 scopus 로고    scopus 로고
    • For conciseness, the symbolic notation ∈ C(ℓ ∈ C) means that the plaquette covering (decorated loop ℓ) appears in configuration C
    • For conciseness, the symbolic notation ∈ C(ℓ ∈ C) means that the plaquette covering (decorated loop ℓ) appears in configuration C.
  • 40
    • 20844437086 scopus 로고    scopus 로고
    • Provided we satisfy the conditions on the parameters w, K, and ε, which are: w = w > 0, K ≥ 0, and ε integrable
    • Provided we satisfy the conditions on the parameters w, K, and ε, which are: W = w > 0, K ≥ 0, and ε integrable.
  • 41
    • 20844460299 scopus 로고    scopus 로고
    • To be precise thereare cases when the change in energy, though local cannotbe written directly as a function of the simple rearrangements used in the noninteracting case (e.g., ↔ ). Typically however it is possible to redefine the rearrangements introducing an appropriate "decoration" that bears precisely the amount of information required to compute the energy difference ε. Examples of these decorated rearrangements will be given in Sections 5.2 and 5.3
    • To be precise thereare cases when the change in energy,though local cannotbe written directly as a function of the simple rearrangements used in the noninteracting case (e.g., ↔ ). Typically however it is possible to redefine the rearrangements introducing an appropriate "decoration" that bears precisely the amount of information required to compute the energy difference ε. Examples of these decorated rearrangements will be given in Sections 5.2 and 5.3.
  • 42
    • 20844459495 scopus 로고    scopus 로고
  • 43
    • 20844444760 scopus 로고    scopus 로고
    • ℓ solely from the information contained in ℓ, without need of further knowledge of a configuration C containing ℓ
    • ℓ solely from the information contained in ℓ, without need of further knowledge of a configuration C containing ℓ.
  • 48
    • 20844445115 scopus 로고
    • reported in Kagome workshop (January) unpublished
    • N. Read, reported in Kagome workshop (January 1992), unpublished
    • (1992)
    • Read, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.