-
1
-
-
33744631045
-
-
See, e.g., PRLTAO 0031-9007 10.1103/PhysRevLett.62.1694
-
See, e.g., N. Read and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.1694 62, 1694 (1989);
-
(1989)
Phys. Rev. Lett.
, vol.62
, pp. 1694
-
-
Read, N.1
Sachdev, S.2
-
2
-
-
0001441341
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.71.169
-
A. V. Chubukov and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.169 71, 169 (1993);
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 169
-
-
Chubukov, A.V.1
Sachdev, S.2
-
3
-
-
0000805607
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.70.3147
-
J. Miller and D. A. Huse, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.3147 70, 3147 (1993).
-
(1993)
Phys. Rev. Lett.
, vol.70
, pp. 3147
-
-
Miller, J.1
Huse, D.A.2
-
4
-
-
84914260693
-
-
See, e.g., PHSTER 0281-1847
-
See, e.g., J. A. Hertz, Phys. Scr., T PHSTER 0281-1847 T10, 1 (1985) and references therein.
-
(1985)
Phys. Scr., T
, vol.10
, pp. 1
-
-
Hertz, J.A.1
-
5
-
-
0000783195
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.61.1294
-
H. P. Wei, D. C. Tsui, M. A. Paalanen, and A. M. M. Pruisken, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.1294 61, 1294 (1988);
-
(1988)
Phys. Rev. Lett.
, vol.61
, pp. 1294
-
-
Wei, H.P.1
Tsui, D.C.2
Paalanen, M.A.3
Pruisken, A.M.M.4
-
6
-
-
0000861777
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.61.1297
-
A. M. M. Pruisken, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 61.1297 61, 1297 (1988);
-
(1988)
Phys. Rev. Lett.
, vol.61
, pp. 1297
-
-
Pruisken, A.M.M.1
-
8
-
-
4243088396
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.62.86
-
N. Read, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.86 62, 86 (1989);
-
(1989)
Phys. Rev. Lett.
, vol.62
, pp. 86
-
-
Read, N.1
-
9
-
-
4243604108
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.70.1501
-
X.-G. Wen and Y.-S. Wu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1501 70, 1501 (1993).
-
(1993)
Phys. Rev. Lett.
, vol.70
, pp. 1501
-
-
Wen, X.-G.1
Wu, Y.-S.2
-
10
-
-
0040793613
-
-
See, e.g., RMPHAT 0034-6861 10.1103/RevModPhys.57.287
-
See, e.g., P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.57.287 57, 287 (1985).
-
(1985)
Rev. Mod. Phys.
, vol.57
, pp. 287
-
-
Lee, P.A.1
Ramakrishnan, T.V.2
-
11
-
-
3342969241
-
-
See, e.g., PRLTAO 0031-9007 10.1103/PhysRevLett.62.2180
-
See, e.g., D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.2180 62, 2180 (1989);
-
(1989)
Phys. Rev. Lett.
, vol.62
, pp. 2180
-
-
Haviland, D.B.1
Liu, Y.2
Goldman, A.M.3
-
12
-
-
4243686384
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.65.927
-
A. F. Hebard and M. A. Paalanen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.927 65, 927 (1990);
-
(1990)
Phys. Rev. Lett.
, vol.65
, pp. 927
-
-
Hebard, A.F.1
Paalanen, M.A.2
-
13
-
-
0001484757
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.65.923
-
M. P. A. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 65.923 65, 923 (1990);
-
(1990)
Phys. Rev. Lett.
, vol.65
, pp. 923
-
-
Fisher, M.P.A.1
-
14
-
-
0032209652
-
-
see also PHTOAD 0031-9228
-
see also A. M. Goldman and N. Markovic, Phys. Today PHTOAD 0031-9228 51 (11), 39 (1998), and references therein.
-
(1998)
Phys. Today
, vol.51
, Issue.11
, pp. 39
-
-
Goldman, A.M.1
Markovic, N.2
-
15
-
-
33645215486
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.40.546
-
M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.546 40, 546 (1989).
-
(1989)
Phys. Rev. B
, vol.40
, pp. 546
-
-
Fisher, M.P.A.1
Weichman, P.B.2
Grinstein, G.3
Fisher, D.S.4
-
17
-
-
4244066733
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.75.4075
-
K. Sheshadri, H. R. Krishnamurthy, R. Pandit, and T. V. Ramakrishnan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.4075 75, 4075 (1995). The mean-field approximation fails to produce a Bose glass phase except as a line separating the Mott insulating and superfluid phases. It does, however, produce a region of quasilocalized superfluid phase, with exponentially small couplings between well separated superfluid droplets, which should be the seed of the Bose glass phase, and thus cross over to the truly localized nonsuperfluid phase, when fluctuations about the mean-field ground state are taken into account.
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 4075
-
-
Sheshadri, K.1
Krishnamurthy, H.R.2
Pandit, R.3
Ramakrishnan, T.V.4
-
18
-
-
84913051924
-
-
EULEEJ 0295-5075 10.1209/0295-5075/24/7/007
-
J. K. Freericks and H. Monien, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/24/7/007 24, 545 (1994);
-
(1994)
Europhys. Lett.
, vol.24
, pp. 545
-
-
Freericks, J.K.1
Monien, H.2
-
19
-
-
0001202631
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.53.2691
-
J. K. Freericks and H. Monien, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.2691 53, 2691 (1996);
-
(1996)
Phys. Rev. B
, vol.53
, pp. 2691
-
-
Freericks, J.K.1
Monien, H.2
-
21
-
-
4243740512
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.73.6
-
Y. Tu and P. B. Weichman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.6 73, 6 (1994);
-
(1994)
Phys. Rev. Lett.
, vol.73
, pp. 6
-
-
Tu, Y.1
Weichman, P.B.2
-
22
-
-
0006783532
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.49.4043
-
Y. B. Kim and X. G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.4043 49, 4043 (1994);
-
(1994)
Phys. Rev. B
, vol.49
, pp. 4043
-
-
Kim, Y.B.1
Wen, X.G.2
-
23
-
-
0034895845
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.64.024517
-
M. B. Hastings, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.024517 64, 024517 (2001).
-
(2001)
Phys. Rev. B
, vol.64
, pp. 024517
-
-
Hastings, M.B.1
-
24
-
-
0001593287
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.45.4855
-
L. Zhang and M. Ma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45. 4855 45, 4855 (1992);
-
(1992)
Phys. Rev. B
, vol.45
, pp. 4855
-
-
Zhang, L.1
Ma, M.2
-
25
-
-
0001643708
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.46.3002
-
K. G. Singh and D. S. Rokhsar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.3002 46, 3002 (1992).
-
(1992)
Phys. Rev. B
, vol.46
, pp. 3002
-
-
Singh, K.G.1
Rokhsar, D.S.2
-
26
-
-
0001219421
-
-
Many authors have explored various models in one and two dimensions using quantum Monte Carlo techniques: See, e.g., PRLTAO 0031-9007 10.1103/PhysRevLett.66.3144
-
Many authors have explored various models in one and two dimensions using quantum Monte Carlo techniques: See, e.g., R. T. Scalettar, G. G. Batrouni, and G. T. Zimanyi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.3144 66, 3144 (1991);
-
(1991)
Phys. Rev. Lett.
, vol.66
, pp. 3144
-
-
Scalettar, R.T.1
Batrouni, G.G.2
Zimanyi, G.T.3
-
28
-
-
0001397388
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.49.12115
-
M. Wallin, E. S. Sørensen, S. M. Girvin, and A. P. Young, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.12115 49, 12115 (1994);
-
(1994)
Phys. Rev. B
, vol.49
, pp. 12115
-
-
Wallin, M.1
Sørensen, E.S.2
Girvin, S.M.3
Young, A.P.4
-
29
-
-
0000508037
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.74.1500
-
S. Zhang, N. Kawashima, J. Carlson, and J. E. Gubernatis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1500 74, 1500 (1995);
-
(1995)
Phys. Rev. Lett.
, vol.74
, pp. 1500
-
-
Zhang, S.1
Kawashima, N.2
Carlson, J.3
Gubernatis, J.E.4
-
30
-
-
0038732480
-
-
PLEEE8 1063-651X 10.1103/PhysRevE.67.015701
-
F. Alet and E. S. Sørensen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.015701 67, 015701 (R) (2003);
-
(2003)
Phys. Rev. e
, vol.67
, pp. 015701
-
-
Alet, F.1
Sørensen, E.S.2
-
31
-
-
1242352112
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.92.015703
-
N. Prokof'ev and B. Svistunov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.015703 92, 015703 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.92
, pp. 015703
-
-
Prokof'Ev, N.1
Svistunov, B.2
-
32
-
-
3643074068
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.71.2307
-
M. Makivic, N. Trivedi, and S. Ullah, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.2307 71, 2307 (1993).
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 2307
-
-
Makivic, M.1
Trivedi, N.2
Ullah, S.3
-
33
-
-
7244225891
-
-
There is, however, some argument over the interpretation of the unusual values of the exponents obtained in this work: see PRLTAO 0031-9007 10.1103/PhysRevLett.74.1038
-
There is, however, some argument over the interpretation of the unusual values of the exponents obtained in this work: see P. B. Weichman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1038 74, 1038 (1995);
-
(1995)
Phys. Rev. Lett.
, vol.74
, pp. 1038
-
-
Weichman, P.B.1
-
34
-
-
7244227424
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.74.1039
-
N. Trivedi and M. Makivic, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1039 74, 1039 (1995).
-
(1995)
Phys. Rev. Lett.
, vol.74
, pp. 1039
-
-
Trivedi, N.1
Makivic, M.2
-
35
-
-
0035842211
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.87.247006
-
J.-W. Lee, M.-C. Cha, and D. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.247006 87, 247006 (2001);
-
(2001)
Phys. Rev. Lett.
, vol.87
, pp. 247006
-
-
Lee, J.-W.1
Cha, M.-C.2
Kim, D.3
-
36
-
-
33644552138
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.72.212515
-
J.-W. Lee and M.-C. Cha, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.212515 72, 212515 (2005).
-
(2005)
Phys. Rev. B
, vol.72
, pp. 212515
-
-
Lee, J.-W.1
Cha, M.-C.2
-
37
-
-
33748679725
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.97.115703
-
A. Priyadarshee, S. Chandrasekharan, J.-W. Lee, and H. U. Baranger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.115703 97, 115703 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 115703
-
-
Priyadarshee, A.1
Chandrasekharan, S.2
Lee, J.-W.3
Baranger, H.U.4
-
38
-
-
0000148254
-
-
PYLAAG 0375-9601 10.1016/0375-9601(80)90604-0
-
S. N. Dorogovtsev, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(80) 90604-0 76A, 169 (1980);
-
(1980)
Phys. Lett.
, vol.76
, pp. 169
-
-
Dorogovtsev, S.N.1
-
39
-
-
0000605284
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.26.154
-
D. Boyanovsky and J. L. Cardy, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.26.154 26, 154 (1982);
-
(1982)
Phys. Rev. B
, vol.26
, pp. 154
-
-
Boyanovsky, D.1
Cardy, J.L.2
-
40
-
-
4243231628
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.27.6971.2
-
D. Boyanovsky and J. L. Cardy, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.27.6971.2 27, 6971 (E) (1983);
-
(1983)
Phys. Rev. B
, vol.27
, pp. 6971
-
-
Boyanovsky, D.1
Cardy, J.L.2
-
41
-
-
0012673134
-
-
JPSOAW 0022-3719 10.1088/0022-3719/17/10/007
-
I. D. Lawrie and V. V. Prudvikov, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/10/007 17, 1655 (1984).
-
(1984)
J. Phys. C
, vol.17
, pp. 1655
-
-
Lawrie, I.D.1
Prudvikov, V.V.2
-
42
-
-
0001445706
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.40.813
-
P. B. Weichman and K. Kim, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.813 40, 813 (1989).
-
(1989)
Phys. Rev. B
, vol.40
, pp. 813
-
-
Weichman, P.B.1
Kim, K.2
-
43
-
-
0003451591
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.76.2977
-
R. Mukhopadhyay and P. B. Weichman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2977 76, 2977 (1996).
-
(1996)
Phys. Rev. Lett.
, vol.76
, pp. 2977
-
-
Mukhopadhyay, R.1
Weichman, P.B.2
-
44
-
-
19644400596
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.150402
-
E. Altman, Y. Kafri, A. Polkovnikov, and G. Refael, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.150402 93, 150402 (2004);
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 150402
-
-
Altman, E.1
Kafri, Y.2
Polkovnikov, A.3
Refael, G.4
-
45
-
-
43049144968
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.100.170402
-
E. Altman, Y. Kafri, A. Polkovnikov, and G. Refael, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.170402 100, 170402 (2008).
-
(2008)
Phys. Rev. Lett.
, vol.100
, pp. 170402
-
-
Altman, E.1
Kafri, Y.2
Polkovnikov, A.3
Refael, G.4
-
46
-
-
0542371301
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.57.1303
-
I. F. Herbut, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.57.1303 57, 1303 (1998).
-
(1998)
Phys. Rev. B
, vol.57
, pp. 1303
-
-
Herbut, I.F.1
-
47
-
-
0001680728
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.58.971
-
I. F. Herbut, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.971 58, 971 (1998). The 1+ expansion developed here consists of computing the RG flows in one dimension, and inserting the engineering dimensions to generalize the recursion relations to higher dimensions. However, in the absence of a form for the Hamiltonian for noninteger d>1, there is presently no rigorous support for this approach.
-
(1998)
Phys. Rev. B
, vol.58
, pp. 971
-
-
Herbut, I.F.1
-
48
-
-
33646068741
-
-
Further neighbor interactions substantially increase the complexity of the phase diagram in the absence of the random site energies, i. One can, in principle, generate Mott insulating phases with arbitrary rational densities ("charge density wave" states). The superfluid transitions from these states are surprisingly complex: for a review, see PTPSEP 0375-9687 10.1143/PTPS.160.314
-
Further neighbor interactions substantially increase the complexity of the phase diagram in the absence of the random site energies, i. One can, in principle, generate Mott insulating phases with arbitrary rational densities ("charge density wave" states). The superfluid transitions from these states are surprisingly complex: for a review, see L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Prog. Theor. Phys. Suppl. PTPSEP 0375-9687 10.1143/PTPS.160.314 160, 314 (2005).
-
(2005)
Prog. Theor. Phys. Suppl.
, vol.160
, pp. 314
-
-
Balents, L.1
Bartosch, L.2
Burkov, A.3
Sachdev, S.4
Sengupta, K.5
-
49
-
-
26944456270
-
-
Generically, only the integer fillings are stable against small disorder since the fractional fillings necessarily break the lattice translation symmetry, leading to multiply degenerate ground states related by a discrete translation. It is not hard to see that arbitrarily small random i will always generate rare regions where it is energetically favorable to form two such states with a domain wall between. If one allows further neighbor hopping matrix elements, Jij, with various signs, one can also generate supersolid phases, which break both lattice translational symmetry and XY -phase symmetry, i.e., superfluid charge density waves: for some recent work, see, e.g., PRLTAO 0031-9007 10.1103/PhysRevLett.94.207202
-
Generically, only the integer fillings are stable against small disorder since the fractional fillings necessarily break the lattice translation symmetry, leading to multiply degenerate ground states related by a discrete translation. It is not hard to see that arbitrarily small random i will always generate rare regions where it is energetically favorable to form two such states with a domain wall between. If one allows further neighbor hopping matrix elements, Jij, with various signs, one can also generate supersolid phases, which break both lattice translational symmetry and XY -phase symmetry, i.e., superfluid charge density waves: for some recent work, see, e.g., P. Sengupta, L. P. Pryadko, F. Alet, M. Troyer, and G. Schmid, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.207202 94, 207202 (2005);
-
(2005)
Phys. Rev. Lett.
, vol.94
, pp. 207202
-
-
Sengupta, P.1
Pryadko, L.P.2
Alet, F.3
Troyer, M.4
Schmid, G.5
-
50
-
-
33747832245
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.97.087209
-
G. G. Batrouni, F. Hébert, and R. T. Scalettar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.087209 97, 087209 (2006), and references therein.
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 087209
-
-
Batrouni, G.G.1
Hébert, F.2
Scalettar, R.T.3
-
51
-
-
0003448505
-
-
See, e.g., McGraw-Hill, New York
-
See, e.g., A. L. Fetter and J. D. Walecka, Quantum Theory of Many Particle Systems (McGraw-Hill, New York, 1971), Chaps. and.
-
(1971)
Quantum Theory of Many Particle Systems
-
-
Fetter, A.L.1
Walecka, J.D.2
-
52
-
-
45749108159
-
-
For a more modern view, see Ref. below.
-
For a more modern view, see Ref. below.
-
-
-
-
53
-
-
13044268246
-
-
See, e.g., PLRBAQ 0556-2805 10.1103/PhysRevB.16.1217
-
See, e.g., J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.16.1217 16, 1217 (1977), and references therein.
-
(1977)
Phys. Rev. B
, vol.16
, pp. 1217
-
-
Jose, J.V.1
Kadanoff, L.P.2
Kirkpatrick, S.3
Nelson, D.R.4
-
54
-
-
0007036853
-
-
This idea has been used to explain the vanishing of the Hall conductivity at magnetic field-tuned superconducting transitions: See PHYADX 0378-4371 10.1016/0378-4371(91)90200-V
-
This idea has been used to explain the vanishing of the Hall conductivity at magnetic field-tuned superconducting transitions: See M. P. A. Fisher, Physica A PHYADX 0378-4371 10.1016/0378-4371(91)90200-V 177, 553 (1991);
-
(1991)
Physica a
, vol.177
, pp. 553
-
-
Fisher, M.P.A.1
-
55
-
-
4043183915
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.68.694
-
A. T. Dorsey and M. P. A. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.694 68, 694 (1992).
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 694
-
-
Dorsey, A.T.1
Fisher, M.P.A.2
-
56
-
-
4244143206
-
-
In d=1, arbitrarily weak hopping disorder in the spin- 1 2 XXZ chain with vanishing axial magnetic field (Ref.) leads to an insulating phase consisting of bound (ferromagnetic) singlet pairs-a random singlet glass: see PRBMDO 0163-1829 10.1103/PhysRevB.50.3799
-
In d=1, arbitrarily weak hopping disorder in the spin- 1 2 XXZ chain with vanishing axial magnetic field (Ref.) leads to an insulating phase consisting of bound (ferromagnetic) singlet pairs-a random singlet glass: see D. S. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.3799 50, 3799 (1994). In the 1D boson problem, this means that the superfluid transition takes place at finite J0,c (u∼ k) >0 even at half-integer filling, (Ref.), and Fig. 1 must be adjusted accordingly, with a line of random singlet glass [identified by both an infinite superfluid susceptibility, (Ref.), and an infinite compressibility, κ→∞ (Ref.)] at μ∼ = μ∼ k on the interval 0≤ J0 < J0,c (μ∼ k).
-
(1994)
Phys. Rev. B
, vol.50
, pp. 3799
-
-
Fisher, D.S.1
-
57
-
-
0346365713
-
-
In the limit of small J0/U0, only site occupancies of k and k+1 contribute between Mott lobes, and Eq. 1.1 or 1.2 may be mapped onto a spin- 1 2 XXZ model H1/2 =- ∑i,j Jij [σ ix σ jx + σ iy σ jy] -h i σiz, in which h μ- (k+ 1 2) U0 vanishes at half-filling [see, Ref., as well as 10.1088/0034-4885/30/2/306 0034-4885 RPPHAG
-
In the limit of small J0 / U0, only site occupancies of k and k+1 contribute between Mott lobes, and Eq. 1.1 or 1.2 may be mapped onto a spin- 1 2 XXZ model H1/2 =- ∑i,j Jij [σ ix σ jx + σ iy σ jy] -h i σiz, in which μ- (k+ 1 2) U0 vanishes at half-filling [see, Ref., as well as M. E. Fisher, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/30/ 2/306 30, 615 (1967)]. If h=0, the energetics, for d>1 (Ref.), favors spins aligned in the plane. So long as the model is not singular, in the sense that there is finite probability p0 that a given Jij, vanishes, the model will have a long-range superfluid order, ψ0 [σ ix +i σiy ] av ≠0. Moreover, in this J0 / U0 →0 limit, J0 is the only energy scale, and the quantum state must be independent of J0, showing that superfluidity survives for arbitrarily small J0. If p0 lies above the bond percolation threshold, the lattice will break up into finite, noncommunicating droplets, and bulk superfluidity is suppressed entirely. For nonzero h, roughly speaking, those sites where h/ J̄ i lies above some threshold of order unity, where J̄ i = 1 2 j Jij, will align with h along z (or -z, for h<0). For sufficiently large h, depending on the precise distribution of Jij, the z -aligned spin clusters will percolate, and superfluidity will be destroyed. The resulting state is the spin- 1 2 analog of the Bose glass phase, and the remaining isolated planar ordered clusters (those with anomalously small h/ J̄ i) are the superfluid droplets of Sec. 3. The two Mott phases correspond to h sufficiently large that all spins are z aligned (or antialigned).
-
(1967)
Rep. Prog. Phys.
, vol.30
, pp. 615
-
-
Fisher, M.E.1
-
58
-
-
0001745236
-
-
For a detailed discussion of the onset transition, see, e.g., PRBMDO 0163-1829 10.1103/PhysRevB.38.8739
-
For a detailed discussion of the onset transition, see, e.g., P. B. Weichman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.8739 38, 8739 (1988).
-
(1988)
Phys. Rev. B
, vol.38
, pp. 8739
-
-
Weichman, P.B.1
-
59
-
-
4243634560
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.61.1847
-
D. S. Fisher and M. P. A. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.1847 61, 1847 (1988).
-
(1988)
Phys. Rev. Lett.
, vol.61
, pp. 1847
-
-
Fisher, D.S.1
Fisher, M.P.A.2
-
60
-
-
34547308803
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.245701
-
P. B. Weichman and R. Mukhopadhyay, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.245701 98, 245701 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 245701
-
-
Weichman, P.B.1
Mukhopadhyay, R.2
-
61
-
-
0014667053
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.23.17
-
R. B. Griffiths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 23.17 23, 17 (1969).
-
(1969)
Phys. Rev. Lett.
, vol.23
, pp. 17
-
-
Griffiths, R.B.1
-
62
-
-
0002990025
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.32.447
-
M. E. Fisher and V. Privman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.32.447 32, 447 (1985).
-
(1985)
Phys. Rev. B
, vol.32
, pp. 447
-
-
Fisher, M.E.1
Privman, V.2
-
63
-
-
0000052917
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.37.4936
-
D. S. Fisher and P. C. Hohenberg, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.37.4936 37, 4936 (1988).
-
(1988)
Phys. Rev. B
, vol.37
, pp. 4936
-
-
Fisher, D.S.1
Hohenberg, P.C.2
-
64
-
-
35949034972
-
-
There are dynamical scaling breakdown issues at the finite T lambda transition [described by the classical model F equations: RMPHAT 0034-6861 10.1103/RevModPhys.49.435
-
There are dynamical scaling breakdown issues at the finite T lambda transition [described by the classical model F equations: P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.49.435 49, 435 (1977)]
-
(1977)
Rev. Mod. Phys.
, vol.49
, pp. 435
-
-
Hohenberg, P.C.1
Halperin, B.I.2
-
65
-
-
0001445753
-
-
as well, where the finite κ argument now yields z=d/2. However, violations are possible (and believed to occur in d=3) where there exist two different dynamical exponents z1 and z2 satisfying z1 + z2 =d. Only the mean (z1 + z2) /2=d/2 enters the corresponding hydrodynamic correlation function [PRBMDO 0163-1829 10.1103/PhysRevB.44.2697
-
as well, where the finite κ argument now yields z=d/2. However, violations are possible (and believed to occur in d=3) where there exist two different dynamical exponents z1 and z2 satisfying z1 + z2 =d. Only the mean (z1 + z2) /2=d/2 enters the corresponding hydrodynamic correlation function [V. Dohm, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.44.2697 44, 2697 (1991)].
-
(1991)
Phys. Rev. B
, vol.44
, pp. 2697
-
-
Dohm, V.1
-
66
-
-
0000983693
-
-
No nonuniversal amplitude A is required in this formulation due to quantum hyperuniversality: See PRBMDO 0163-1829 10.1103/PhysRevB.43.13583
-
No nonuniversal amplitude A is required in this formulation due to quantum hyperuniversality: See K. Kim and P. B. Weichman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.43.13583 43, 13583 (1991).
-
(1991)
Phys. Rev. B
, vol.43
, pp. 13583
-
-
Kim, K.1
Weichman, P.B.2
-
67
-
-
24244445660
-
-
The definition of the superfluid density 4.8 in terms of finite-size scaling of twisted boundary conditions was first proposed by PLRAAN 1050-2947 10.1103/PhysRevA.8.1111
-
The definition of the superfluid density 4.8 in terms of finite-size scaling of twisted boundary conditions was first proposed by M. E. Fisher, M. N. Barber, and D. Jasnow, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.8.1111 8, 1111 (1973). Amazingly, the last section of this paper, containing a discussion of how finite-size scaling might lead to violations of the Josephson relation, proposes a mechanism very similar to ours: anomalously strong boundary condition dependence of tθ, the distance from the critical point, on the twist wave vector, k0. If tθ -t∼ k02, they find υ=1-α. Here we find an even more anomalous linear dependence of δθ -δ on ω0, leading to υτ =-α. We are unaware of any classical model where the original proposed violation occurs, but a candidate would presumably be a transition between two different phases with finite superfluid density.
-
(1973)
Phys. Rev. a
, vol.8
, pp. 1111
-
-
Fisher, M.E.1
Barber, M.N.2
Jasnow, D.3
-
68
-
-
4243944881
-
-
A famous theorem [PRLTAO 0031-9007 10.1103/PhysRevLett.57.2999
-
A famous theorem [J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.57.2999 57, 2999 (1986);
-
(1986)
Phys. Rev. Lett.
, vol.57
, pp. 2999
-
-
Chayes, J.T.1
Chayes, L.2
Fisher, D.S.3
Spencer, T.4
-
69
-
-
33646646291
-
-
CMPHAY 0010-3616 10.1007/BF01225510
-
J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01225510 120, 501 (1989)] requires that νfs >2/d, where νfs is a correlation exponent defined through finite-size scaling, and it is commonly assumed that under most conditions that ν= νfs.
-
(1989)
Commun. Math. Phys.
, vol.120
, pp. 501
-
-
Chayes, J.T.1
Chayes, L.2
Fisher, D.S.3
Spencer, T.4
-
70
-
-
0001400859
-
-
However, it has been argued more recently [PRLTAO 0031-9007 10.1103/PhysRevLett.79.5130
-
However, it has been argued more recently [F. Pazmandi, R. T. Scalettar, and G. T. Zimanyi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.5130 79, 5130 (1997)] that νfs generally places no constraints on the value of ν. Nevertheless, analytic results in d=1 (Ref.) and quantum Monte Carlo data in d=2 (Ref.) are consistent with this inequality.
-
(1997)
Phys. Rev. Lett.
, vol.79
, pp. 5130
-
-
Pazmandi, F.1
Scalettar, R.T.2
Zimanyi, G.T.3
-
71
-
-
84956109971
-
-
EULEEJ 0295-5075 10.1209/0295-5075/3/12/007
-
T. Giamarchi and H. J. Schulz, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/3/12/007 3, 1287 (1987);
-
(1987)
Europhys. Lett.
, vol.3
, pp. 1287
-
-
Giamarchi, T.1
Schulz, H.J.2
-
72
-
-
8644272071
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.37.325
-
T. Giamarchi and H. J. Schulz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.37.325 37, 325 (1988).
-
(1988)
Phys. Rev. B
, vol.37
, pp. 325
-
-
Giamarchi, T.1
Schulz, H.J.2
-
74
-
-
0000359165
-
-
See, e.g., PLRBAQ 0556-2805 10.1103/PhysRevB.12.1038
-
See, e.g., A. Aharony, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.12. 1038 12, 1038 (1975);
-
(1975)
Phys. Rev. B
, vol.12
, pp. 1038
-
-
Aharony, A.1
-
75
-
-
85104369179
-
-
see also in edited by C. Domb and M. S. Green (Academic, London
-
see also in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M. S. Green, (Academic, London, 1976), Vol. 6, Chap..
-
(1976)
Phase Transitions and Critical Phenomena
, vol.6
-
-
-
76
-
-
0001898814
-
-
See, e.g., PRPLCM 0370-1573 10.1016/0370-1573(74)90023-4
-
See, e.g., K. G. Wilson and J. Kogut, Phys. Rep., Phys. Lett. PRPLCM 0370-1573 10.1016/0370-1573(74)90023-4 12C, 75 (1974).
-
(1974)
Phys. Rep., Phys. Lett.
, vol.12
, pp. 75
-
-
Wilson, K.G.1
Kogut, J.2
-
77
-
-
0000162933
-
-
See, e.g., PTPKAV 0033-068X 10.1143/PTP.56.1454
-
See, e.g., M. Suzuki, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.56.1454 56, 1454 (1976).
-
(1976)
Prog. Theor. Phys.
, vol.56
, pp. 1454
-
-
Suzuki, M.1
-
78
-
-
4243596165
-
-
See, e.g. PRLTAO 0031-9007 10.1103/PhysRevLett.69.828
-
See, e.g., E. S. Sørensen, M. Wallin, S. M. Girvin, and A. P. Young, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.828 69, 828 (1992).
-
(1992)
Phys. Rev. Lett.
, vol.69
, pp. 828
-
-
Sørensen, E.S.1
Wallin, M.2
Girvin, S.M.3
Young, A.P.4
|