-
4
-
-
0038115189
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902
-
G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003).
-
(2003)
Phys. Rev. Lett.
, vol.90
, pp. 227902
-
-
Vidal, G.1
Latorre, J.I.2
Rico, E.3
Kitaev, A.4
-
5
-
-
37649027994
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203
-
H. Fan, V. Korepin, and V. Roychowdhury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203 93, 227203 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 227203
-
-
Fan, H.1
Korepin, V.2
Roychowdhury, V.3
-
6
-
-
34447101731
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.76.012401
-
H. Katsura, T. Hirano, and Y. Hatsugai, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.012401 76, 012401 (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 012401
-
-
Katsura, H.1
Hirano, T.2
Hatsugai, Y.3
-
7
-
-
34547137392
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.76.014428
-
H. Fan, V. Korepin, V. Roychowdhury, C. Hadley, and S. Bose, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.014428 76, 014428 (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 014428
-
-
Fan, H.1
Korepin, V.2
Roychowdhury, V.3
Hadley, C.4
Bose, S.5
-
8
-
-
2442674839
-
-
NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2
-
C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2 424, 443 (1994).
-
(1994)
Nucl. Phys. B
, vol.424
, pp. 443
-
-
Holzhey, C.1
Larsen, F.2
Wilczek, F.3
-
9
-
-
2442560099
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.92.096402
-
V. E. Korepin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 096402 92, 096402 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.92
, pp. 096402
-
-
Korepin, V.E.1
-
11
-
-
33645005950
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.96.100603
-
N. Laflorencie, E. S. Sørensen, M. S. Chang, and I. Affleck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.100603 96, 100603 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 100603
-
-
Laflorencie, N.1
Sørensen, E.S.2
Chang, M.S.3
Affleck, I.4
-
12
-
-
33751215867
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.74.050305
-
H. Q. Zhou, T. Barthel, J. O. Fjærestad, and U. Schollwöck, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.050305 74, 050305 (R) (2006).
-
(2006)
Phys. Rev. A
, vol.74
, pp. 050305
-
-
Zhou, H.Q.1
Barthel, T.2
Fjærestad, J.O.3
Schollwöck, U.4
-
13
-
-
40749141043
-
-
arXiv:0708.2978.
-
For a recent review, see J. Cardy, e-print arXiv:0708.2978.
-
-
-
Cardy, J.1
-
14
-
-
33645813835
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.96.140604
-
H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.140604 96, 140604 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 140604
-
-
Quan, H.T.1
Song, Z.2
Liu, X.F.3
Zanardi, P.4
Sun, C.P.5
-
15
-
-
33749345011
-
-
PLEEE8 1063-651X 10.1103/PhysRevE.74.031123
-
P. Zanardi and N. Paunković, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.031123 74, 031123 (2006).
-
(2006)
Phys. Rev. e
, vol.74
, pp. 031123
-
-
Zanardi, P.1
Paunković, N.2
-
16
-
-
34547869745
-
-
PLEEE8 1063-651X 10.1103/PhysRevE.76.022101
-
W. L. You, Y. W. Li, and S. J. Gu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.022101 76, 022101 (2007).
-
(2007)
Phys. Rev. e
, vol.76
, pp. 022101
-
-
You, W.L.1
Li, Y.W.2
Gu, S.J.3
-
18
-
-
33846604250
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.75.014439
-
M. Cozzini, P. Giorda, and P. Zanardi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.014439 75, 014439 (2007).
-
(2007)
Phys. Rev. B
, vol.75
, pp. 014439
-
-
Cozzini, M.1
Giorda, P.2
Zanardi, P.3
-
19
-
-
34648814053
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.76.104420
-
M. Cozzini, R. Ionicioiu, and P. Zanardi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.104420 76, 104420 (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 104420
-
-
Cozzini, M.1
Ionicioiu, R.2
Zanardi, P.3
-
20
-
-
33947256773
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.110601
-
P. Buonsante and A. Vezzani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.110601 98, 110601 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 110601
-
-
Buonsante, P.1
Vezzani, A.2
-
21
-
-
33947301917
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.75.115119
-
N. Oelkers and J. Links, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.115119 75, 115119 (2007).
-
(2007)
Phys. Rev. B
, vol.75
, pp. 115119
-
-
Oelkers, N.1
Links, J.2
-
22
-
-
34548549064
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.99.100603
-
P. Zanardi, P. Giorda, and M. Cozzini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.100603 99, 100603 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.99
, pp. 100603
-
-
Zanardi, P.1
Giorda, P.2
Cozzini, M.3
-
23
-
-
34548454416
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.99.095701
-
L. Campos Venuti and P. Zanardi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.095701 99, 095701 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.99
, pp. 095701
-
-
Campos Venuti, L.1
Zanardi, P.2
-
25
-
-
37049015409
-
-
PLEEE8 1063-651X 10.1103/PhysRevE.76.061108
-
S. Chen, L. Wang, S. J. Gu, and Y. Wang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.061108 76, 061108 (2007).
-
(2007)
Phys. Rev. e
, vol.76
, pp. 061108
-
-
Chen, S.1
Wang, L.2
Gu, S.J.3
Wang, Y.4
-
28
-
-
40749148407
-
-
arXiv:0704.2945.
-
H. Q. Zhou, e-print arXiv:0704.2945.
-
-
-
Zhou, H.Q.1
-
29
-
-
36049013005
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.76.180403
-
M. F. Yang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.180403 76, 180403 (R) (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 180403
-
-
Yang, M.F.1
-
30
-
-
3442895828
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.69.2863
-
S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69. 2863 69, 2863 (1992);
-
(1992)
Phys. Rev. Lett.
, vol.69
, pp. 2863
-
-
White, S.R.1
-
31
-
-
20044389808
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.48.10345
-
S. R. White, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.10345 48, 10345 (1993);
-
(1993)
Phys. Rev. B
, vol.48
, pp. 10345
-
-
White, S.R.1
-
32
-
-
23844520141
-
-
RMPHAT 0034-6861 10.1103/RevModPhys.77.259
-
U. Schollwöck, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 77.259 77, 259 (2005).
-
(2005)
Rev. Mod. Phys.
, vol.77
, pp. 259
-
-
Schollwöck, U.1
-
33
-
-
35949018843
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.34.6372
-
H. J. Schulz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.6372 34, 6372 (1986).
-
(1986)
Phys. Rev. B
, vol.34
, pp. 6372
-
-
Schulz, H.J.1
-
34
-
-
7244220861
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.40.4709
-
M. den Nijs and K. Rommelse, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.4709 40, 4709 (1989).
-
(1989)
Phys. Rev. B
, vol.40
, pp. 4709
-
-
Den Nijs, M.1
Rommelse, K.2
-
35
-
-
0038756041
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.67.104401
-
W. Chen, K. Hida, and B. C. Sanctuary, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.104401 67, 104401 (2003).
-
(2003)
Phys. Rev. B
, vol.67
, pp. 104401
-
-
Chen, W.1
Hida, K.2
Sanctuary, B.C.3
-
36
-
-
10644277555
-
-
EPJBFY 1434-6028 10.1140/epjb/e2003-00299-7
-
C. Degli Esposti Boschi, E. Ercolessi, F. Ortolani, and M. Roncaglia, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2003-00299-7 35, 465 (2003).
-
(2003)
Eur. Phys. J. B
, vol.35
, pp. 465
-
-
Degli Esposti Boschi, C.1
Ercolessi, E.2
Ortolani, F.3
Roncaglia, M.4
-
37
-
-
33749032091
-
-
EPJBFY 1434-6028 10.1140/epjb/e2006-00342-3
-
L. Campos Venuti, C. Degli Esposti Boschi, E. Ercolessi, G. Morandi, F. Ortolani, S. Pasini, and M. Roncaglia, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2006-00342-3 53, 11 (2006).
-
(2006)
Eur. Phys. J. B
, vol.53
, pp. 11
-
-
Campos Venuti, L.1
Degli Esposti Boschi, C.2
Ercolessi, E.3
Morandi, G.4
Ortolani, F.5
Pasini, S.6
Roncaglia, M.7
-
38
-
-
40749091147
-
-
Here we use the notations of Ref..
-
Here we use the notations of Ref..
-
-
-
-
39
-
-
0031548107
-
-
NUPBBO 0550-3213 10.1016/S0550-3213(97)00123-5
-
S. Lukyanov and A. Zamolodchikov, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(97)00123-5 493, 571 (1997).
-
(1997)
Nucl. Phys. B
, vol.493
, pp. 571
-
-
Lukyanov, S.1
Zamolodchikov, A.2
-
40
-
-
40749158617
-
-
To lift the double degeneracy in the Néel phase, a Zeeman term h1 S1z acting only upon the spin at site 1 is added in the Hamiltonian of Eq. 2. Here we take the boundary magnetic field h1 =-0.01. The inclusion of this tiny Zeeman splitting selects a specific ground state and stabilizes our calculations of the fidelity in the Néel phase. Nevertheless, this term is found to have no significant effect on the entanglement entropy and the fidelity in other phases.
-
To lift the double degeneracy in the Néel phase, a Zeeman term h1 S1z acting only upon the spin at site 1 is added in the Hamiltonian of Eq. 2. Here we take the boundary magnetic field h1 =-0.01. The inclusion of this tiny Zeeman splitting selects a specific ground state and stabilizes our calculations of the fidelity in the Néel phase. Nevertheless, this term is found to have no significant effect on the entanglement entropy and the fidelity in other phases.
-
-
-
-
41
-
-
40749106467
-
-
The DMRG method had been used to calculate the overlap of two different ground states for a decade. For example, people had applied this technique to evaluate the exponent of the orthogonality catastrophe for the problem of a single impurity in a one-dimensional Luttinger liquid.
-
The DMRG method had been used to calculate the overlap of two different ground states for a decade. For example, people had applied this technique to evaluate the exponent of the orthogonality catastrophe for the problem of a single impurity in a one-dimensional Luttinger liquid.
-
-
-
-
42
-
-
0001234057
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.54.R9643
-
S. Qin, M. Fabrizio, and L. Yu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.R9643 54, R9643 (1996);
-
(1996)
Phys. Rev. B
, vol.54
, pp. 9643
-
-
Qin, S.1
Fabrizio, M.2
Yu, L.3
-
43
-
-
0000011890
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.56.9766
-
S. Qin, M. Fabrizio, L. Yu, M. Oshikawa, and I. Affleck, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.56.9766 56, 9766 (1997).
-
(1997)
Phys. Rev. B
, vol.56
, pp. 9766
-
-
Qin, S.1
Fabrizio, M.2
Yu, L.3
Oshikawa, M.4
Affleck, I.5
-
44
-
-
35948966063
-
-
For a recent review, see ZZZZZZ 1742-5468
-
For a recent review, see I. P. McCulloch, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 2007, P10014.
-
J. Stat. Mech.: Theory Exp.
, vol.2007
, pp. 10014
-
-
McCulloch, I.P.1
-
45
-
-
0001574528
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.28.1516
-
M. E. Fisher and M. N. Barber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28.1516 28, 1516 (1972);
-
(1972)
Phys. Rev. Lett.
, vol.28
, pp. 1516
-
-
Fisher, M.E.1
Barber, M.N.2
-
46
-
-
0001315226
-
-
edited by C. Domb and J. L. Lebowitz (Academic Press, London
-
M. N. Barber, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic Press, London, 1983), Vol. 8, p. 145.
-
(1983)
Phase Transitions and Critical Phenomena
, vol.8
, pp. 145
-
-
Barber, M.N.1
-
47
-
-
40749118797
-
-
We note that the DMRG calculations in Refs. and are under the periodic boundary conditions, rather than the open boundary conditions used in the present work. The small discrepancy of our results from theirs may be due to the different boundary conditions employed.
-
We note that the DMRG calculations in Refs. and are under the periodic boundary conditions, rather than the open boundary conditions used in the present work. The small discrepancy of our results from theirs may be due to the different boundary conditions employed.
-
-
-
|