Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

Annals of Physics

Volumn 322, Issue 4, 2007, Pages 903-934

  Castelnovo, Claudio ^a   Chamon, Claudio ^a   Mudry, Christopher ^b   Pujol, Pierre ^c  

^a Boston University   (United States)

^b PAUL SCHERRER INSTITUTE   (Switzerland)

^c Laboratoire de Physique UMR CNRS ENSL   (France)

Author keywords

Conformal field theory; Kosterlitz Thouless transition; Quantum criticality; Quantum dimer model; Stochastic Matrix Form decomposition

Indexed keywords

EID: 33847279441     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2006.04.017     Document Type: Article

References (64)

1. Fowler R.H., and Rushbrooke G.S. Trans. Faraday Soc. 33 (1937) 1272
2. Thurston W. Am. Math. Monthly 97 (1990) 757 Richard Kenyon, Available from: math-ph/0405052
3. Kasteleyn P.W. Physica (Amsterdam) 27 (1961) 1209
4. J. Math. Phys. 4 (1963) 287
5. Fisher M.E. Phys. Rev. 124 (1961) 1664
6. J. Math. Phys. 4 (1963) 278
7. J. Math. Phys. 7 (1966) 1776
8. Fisher M.E., and Stephenson J. Phys. Rev. 132 (1963) 1411
9. Kondev J., and Henley C.L. Phys. Rev. B 52 (1995) 6628
10. Kondev J., and Henley C.L. Nucl. Phys. B 464 (1996) 540
11. Fendley P., Moessner R., and Sondhi S.L. Phys. Rev. B 66 (2002) 214513
12. Krauth W., and Moessner R. Phys. Rev. B 67 (2003) 064503
13. Huse D.A., Krauth W., Moessner R., and Sondhi S.L. Phys. Rev. Lett. 91 (2003) 167004
14. Alet F., Jacobsen J.L., Misguich G., Pasquier V., Mila F., and Troyer M. Phys. Rev. Lett. 94 (2005) 235702
15. Kivelson S.A., Rokhsar D.S., and Sethna J.P. Phys. Rev. B 35 (1987) 8865
16. Rokhsar D.S., and Kivelson S.A. Phys. Rev. Lett. 61 (1988) 2376
17. Levitov L.S. Phys. Rev. Lett. 64 (1990) 92
18. Fradkin E. Field Theories of Condensed Matter Systems (1991), Addison-Wesley, Redwood City Chapter 6
19. Leung P.W., Chiu K.C., and Runge K.J. Phys. Rev. B 54 (1996) 12938
20. Henley C.L. J. Stat. Phys. 89 (1997) 483
21. Moessner R., and Sondhi S.L. Phys. Rev. Lett. 86 (2001) 1881
22. Moessner R., Sondhi S.L., and Chandra P. Phys. Rev. B 64 (2001) 144416
23. Moessner R., Sondhi S.L., and Fradkin E. Phys. Rev. B 65 (2002) 024504
24. Ioselevich A., Ivanov D.A., and Feigelman M.V. Phys. Rev. B 66 (2002) 174405
25. Misguich G., Serban D., and Pasquier V. Phys. Rev. Lett. 89 (2002) 137202
26. Phys. Rev. B 67 (2003) 214413
27. Moessner R., and Sondhi S.L. Phys. Rev. B 68 (2003) 054405
28. Moessner R., and Sondhi S.L. Phys. Rev. B 68 (2003) 184512
29. M. Freedman, C. Nayak, K. Shtengel, Available from: cond-mat/0309120.
30. Hermele M., Fisher M.P.A., and Balents L. Phys. Rev. B 69 (2004) 064404
31. Fradkin E., Huse D.A., Moessner R., Oganesyan V., and Sondhi S.L. Phys. Rev. B 69 (2004) 224415
32. Misguich G., Serban D., and Pasquier V. J. Phys.: Cond. Mat. 16 (2004) S823
33. Henley C.L. J. Phys. C 16 (2004) S891
34. Ardonne E., Fendley P., and Fradkin E. Ann. Phys. (N.Y.) 310 (2004) 493
35. Ivanov D.A. Phys. Rev. B 70 (2004) 094430
36. Misguich G., Pasquier V., Mila F., and Lhuillier C. Phys. Rev. B 71 (2005) 184424
37. Ralko A., Ferrero M., Becca F., Ivanov D., and Mila F. Phys. Rev. B 71 (2005) 224109
38. Castelnovo C., Chamon C., Mudry C., and Pujol P. Ann. Phys. (N.Y.) 318 (2005) 316
39. Raman K.S., Moessner R., and Sondhi S.L. Phys. Rev. B 72 (2005) 064413
40. Freedman M., Nayak C., and Shtengel K. Phys. Rev. Lett. 94 (2005) 066401
41. Syljuåsen O.F. Phys. Rev. B 71 (2005) 020401R
42. Int. Jour. Mod. Phys. B 19 (2005) 1973. Available from: cond-mat/0512579
43. A.W. Sandvik, R. Moessner, Available from: cond-mat/0507277.
44. R. Moessner, K.S. Raman, S.L. Sondhi, Available from: cond-mat/0510498.
45. Bergman D.L., Fiete G.A., and Balents L. Phys. Rev. Lett. 96 (2006) 097207. Available from: cond-mat/0511176
46. Senthil T., Balents L., Sachdev S., Vishwanath A., and Fisher M.P.A. Phys. Rev. B 70 (2004) 144407
47. Balents L., Bartosch L., Burkov A., Sachdev S., and Sengupta K. Phys. Rev. B 71 (2005) 144508 (2005) 144509
48. Chakravarty S. Phys. Rev. B 66 (2002) 224505
49. Castelnovo C., Chamon C., Mudry C., and Pujol P. Phys. Rev. B 73 (2006) 144411
50. Hertz J.A. Phys. Rev. B 14 (1976) 1165
51. Hastings M.B. Phys. Rev. B 69 (2004) 104431
52. Freedman M., Nayak C., and Shtengel K. Phys. Rev. Lett. 94 (2005) 147205
53. Grinstein G. Phys. Rev. B 23 (1981) 4615
54. Ghaemi P., Vishwanath A., and Senthil T. Phys. Rev. B 72 (2005) 024420
55. Shtengel K., Nayak C., Bishara W., and Chamon C. J. Phys. A: Math. Gen. 38 (2005) L589
56. Stefanos Papanikolaou, Erik Luijten, Eduardo Fradkin, abstract N45.00012, APS March meeting 2006, in preparation.
57. .
58. Jacobsen J.L., and Kondev J. Nucl. Phys. B 532 (1998) 635 and references therein
59. 0 (see Section 3.3). This usually signals the presence in the system of fluctuations with a spatial periodicity larger than the one generically allowed by L (two lattice spacings). Choosing L to be a multiple of 4 seems to be sufficient in our case to get rid of this spurious behavior.
60. Castelnovo C., Pujol P., and Chamon C. Phys. Rev. B 69 (2004) 104529
61. Cirillo E.N.M., Gonnella G., and Pelizzola A. Phys. Rev. E 53 (1996) 1479
62. Notice however that the two ordered phases separated by the tricritical point may differ from those in the RK Hamiltonian, if the presence of a resonating valence bond phase was to be confirmed in the latter model.
63. Batista C.D., and Trugman S.A. Phys. Rev. Lett. 93 (2004) 217202
64. D. Poilblanc, F. Alet, F. Becca, A. Ralko, F. Trousselet, F. Mila, Phys. Rev. B (RC), Available from: cond-mat/0602256, submitted for publication.