-
1
-
-
43849112312
-
-
10.1103/RevModPhys.80.517
-
L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008). 10.1103/RevModPhys.80.517
-
(2008)
Rev. Mod. Phys.
, vol.80
, pp. 517
-
-
Amico, L.1
Fazio, R.2
Osterloh, A.3
Vedral, V.4
-
2
-
-
34347407227
-
-
10.1103/PhysRevB.75.214407
-
S. Furukawa and G. Misguich, Phys. Rev. B 75, 214407 (2007). 10.1103/PhysRevB.75.214407
-
(2007)
Phys. Rev. B
, vol.75
, pp. 214407
-
-
Furukawa, S.1
Misguich, G.2
-
5
-
-
73249141480
-
-
10.1103/PhysRevB.80.184421
-
J.-M. Stéphan, S. Furukawa, G. Misguich, and V. Pasquier, Phys. Rev. B 80, 184421 (2009). 10.1103/PhysRevB.80.184421
-
(2009)
Phys. Rev. B
, vol.80
, pp. 184421
-
-
Stéphan, J.-M.1
Furukawa, S.2
Misguich, G.3
Pasquier, V.4
-
6
-
-
77957735403
-
-
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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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.
-
-
-
-
7
-
-
33746922351
-
-
10.1103/PhysRevLett.97.050404
-
E. Fradkin and J. E. Moore, Phys. Rev. Lett. 97, 050404 (2006). 10.1103/PhysRevLett.97.050404
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 050404
-
-
Fradkin, E.1
Moore, J.E.2
-
8
-
-
64349115016
-
-
10.1103/PhysRevB.79.115421
-
B. Hsu, M. Mulligan, E. Fradkin, and E.-A. Kim, Phys. Rev. B 79, 115421 (2009). 10.1103/PhysRevB.79.115421
-
(2009)
Phys. Rev. B
, vol.79
, pp. 115421
-
-
Hsu, B.1
Mulligan, M.2
Fradkin, E.3
Kim, E.-A.4
-
9
-
-
77957735153
-
-
In the quantum point of view, where one studies the entanglement in a RK wave function, the dominant (∼L ) contribution is the boundary (also called "area") law
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In the quantum point of view, where one studies the entanglement in a RK wave function, the dominant (∼ L) contribution is the boundary (also called "area") law.
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-
-
10
-
-
77957737534
-
-
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..
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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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-
-
12
-
-
77957732042
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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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T c = 2 / ln (1 + √ 2) on the square lattice (Refs.) and T c = 4 / ln (3) on the triangular lattice (Ref.).
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14
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77957723624
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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
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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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-
-
-
15
-
-
0036215403
-
-
10.1137/S0097539700377037
-
J. Sawada, SIAM J. Comput. 31, 259 (2001). 10.1137/S0097539700377037
-
(2001)
SIAM J. Comput.
, vol.31
, pp. 259
-
-
Sawada, J.1
-
16
-
-
77957731374
-
-
In fact, the analysis of Sec. suggests that rn ( μc ) flows to its ferromagnetic boundary condition limit, ln(2), as soon as n>1
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In fact, the analysis of Sec. suggests that r n (μ c) flows to its ferromagnetic boundary condition limit, ln(2), as soon as n > 1.
-
-
-
-
19
-
-
36149018057
-
-
10.1103/PhysRev.127.1508
-
S. Katsura, Phys. Rev. 127, 1508 (1962). 10.1103/PhysRev.127.1508
-
(1962)
Phys. Rev.
, vol.127
, pp. 1508
-
-
Katsura, S.1
-
20
-
-
33645161396
-
-
10.1103/PhysRevLett.96.110405
-
M. Levin and X.-G. Wen, Phys. Rev. Lett. 96, 110405 (2006). 10.1103/PhysRevLett.96.110405
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 110405
-
-
Levin, M.1
Wen, X.-G.2
-
21
-
-
33645151438
-
-
10.1103/PhysRevLett.96.110404
-
A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006). 10.1103/PhysRevLett.96.110404
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 110404
-
-
Kitaev, A.1
Preskill, J.2
-
22
-
-
24544453124
-
-
10.1016/0550-3213(89)90521-X
-
J. L. Cardy, Nucl. Phys. B 324, 581 (1989). 10.1016/0550-3213(89)90521-X
-
(1989)
Nucl. Phys. B
, vol.324
, pp. 581
-
-
Cardy, J.L.1
-
26
-
-
77957735537
-
-
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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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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-
-
27
-
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-
) 2, where the field is compactified on a circle of radius R: φ=φ+2πR
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) 2, where the field is compactified on a circle of radius R: φ = φ + 2 π R.
-
-
-
-
28
-
-
77957728170
-
-
arXiv:1007.3789 (unpublished)
-
Mo. Oshikawa, arXiv:1007.3789 (unpublished).
-
-
-
Oshikawa, Mo.1
-
31
-
-
0009317592
-
-
10.1016/S0370-2693(01)00276-3
-
V. B. Petkova and J.-B. Zuber, Phys. Lett. B 504, 157 (2001). 10.1016/S0370-2693(01)00276-3
-
(2001)
Phys. Lett. B
, vol.504
, pp. 157
-
-
Petkova, V.B.1
Zuber, J.-B.2
-
33
-
-
36149012281
-
-
10.1103/PhysRev.65.117
-
L. Onsager, Phys. Rev. 65, 117 (1944). 10.1103/PhysRev.65.117
-
(1944)
Phys. Rev.
, vol.65
, pp. 117
-
-
Onsager, L.1
-
34
-
-
0342690300
-
-
10.1016/0031-8914(50)90130-3
-
R. Houtappel, Physica (Amsterdam) 16, 425 (1950). 10.1016/0031-8914(50) 90130-3
-
(1950)
Physica (Amsterdam)
, vol.16
, pp. 425
-
-
Houtappel, R.1
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