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9
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20844447168
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Available from:
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R. Kenyon. Available from:
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Kenyon, R.1
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20844437267
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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
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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
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35
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20844438506
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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
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See Chapter 5 from Matrices: Theory and Applications, by D. Serre,Springer, New York, 2002.
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(2002)
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36
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20844461333
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See also Chapter A4.1 from Quantum Field Theory and Critical Phenomena, by J.Zinn-Justin,Oxford University Press, New York
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See also Chapter A4.1 from Quantum Field Theory and Critical Phenomena, by J.Zinn-Justin,Oxford University Press,New York, 1996.
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(1996)
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37
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+K(EC′-EC)/2)
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+K(EC′-EC)/2).
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39
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20844454361
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For conciseness, the symbolic notation ∈ C(ℓ ∈ C) means that the plaquette covering (decorated loop ℓ) appears in configuration C
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For conciseness, the symbolic notation ∈ C(ℓ ∈ C) means that the plaquette covering (decorated loop ℓ) appears in configuration C.
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40
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20844437086
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Provided we satisfy the conditions on the parameters w, K, and ε, which are: w = w > 0, K ≥ 0, and ε integrable
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Provided we satisfy the conditions on the parameters w, K, and ε, which are: W = w > 0, K ≥ 0, and ε integrable.
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41
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20844460299
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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
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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.
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42
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20844459495
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ℓ
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ℓ
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43
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20844444760
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ℓ solely from the information contained in ℓ, without need of further knowledge of a configuration C containing ℓ
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ℓ solely from the information contained in ℓ, without need of further knowledge of a configuration C containing ℓ.
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48
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20844445115
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reported in Kagome workshop (January) unpublished
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N. Read, reported in Kagome workshop (January 1992), unpublished
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(1992)
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Read, N.1
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