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Volumn 82, Issue 12, 2010, Pages

Rényi entropy of a line in two-dimensional Ising models

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EID: 77957730272     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.125455     Document Type: Article
Times cited : (90)

References (34)
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    • This quantum/classical correspondence works in a rather straightforward way for simple constrained models (such as dimer models or vertex models). For other models, such as the Ising model considered in this paper, some additional care is needed to define the geometry of the A/B boundary at the microscopic level. In the particular case of 2D classical Ising models, the spins living at the frontier between A and B have to be "duplicated" to insure that the decomposition induced by the classical spin configurations is indeed a proper Schmidt decomposition of the RK state. See Ref. for more details
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    • The field-theory prediction of Ref. is r1 (T= Tc ) =ln (2) and does not agree with our numerical calculations. Remark: r1 corresponds to S0 (x) in the notations of Ref..
    • The field-theory prediction of Ref. is r 1 (T = T c) = ln (2) and does not agree with our numerical calculations. Remark: r 1 corresponds to S 0 (x) in the notations of Ref..
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    • Tc =2/ln (1+√2 ) on the square lattice (Refs.) and Tc =4/ln (3) on the triangular lattice (Ref.)
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    • We also use the property that, for periodic boundary conditions, σiz =1 in the ground state |G. Since we work in the σz basis, this reduces by another factor two the number of probabilities to compute
    • We also use the property that, for periodic boundary conditions, i σ i z = 1 in the ground state | G. Since we work in the σ z basis, this reduces by another factor two the number of probabilities to compute.
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    • The Rényi entropy can be computed for complex values of n and one can detect possible singularities by analyzing the locations of the its zeros in the complex plane, as was done in Ref. for a different model. However, in our case, such an approach does not seem to shed more light on the n=1 issue than the real-axis analysis presented here
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    • ) 2, where the field is compactified on a circle of radius R: φ = φ + 2 π R.
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.