Nonperturbative renormalization group approach to strongly correlated lattice bosons

Physical Review B - Condensed Matter and Materials Physics

Volumn 84, Issue 17, 2011, Pages

  Rancon A ^a,b   Dupuis, N ^a,b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 82455203868     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.84.174513     Document Type: Article

References (79)

1. J. Berges, N. Tetradis, and C. Wetterich, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00098-9 363, 223 (2002).
2. B. Delamotte, e-print arXiv: cond-mat/0702365 (unpublished).
3. T. Machado and N. Dupuis, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.041128 82, 041128 (2010).
4. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.546 40, 546 (1989).
5. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108 81, 3108 (1998).
6. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/415039a 415, 39 (2002). (Pubitemid 34062442)
7. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.130403 92, 130403 (2004).
8. I. B. Spielman, W. D. Phillips, and J. V. Porto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.080404 98, 080404 (2007). (Pubitemid 46326138)
9. B. Capogrosso-Sansone, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.134302 75, 134302 (2007).
10. B. Capogrosso-Sansone, S. G. Söyler, N. Prokof'ev, and B. Svistunov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.015602 77, 015602 (2008). (Pubitemid 351197996)
11. W. Krauth and N. Trivedi, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/14/7/003 14, 627 (1991).
12. N. Dupuis and K. Sengupta, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/80/50007 80, 50007 (2007).
13. N. Dupuis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102. 190401 102, 190401 (2009).
14. N. Dupuis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.043627 80, 043627 (2009).
15. C. Wetterich, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.064504 77, 064504 (2008).
16. S. Floerchinger and C. Wetterich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.053603 77, 053603 (2008). (Pubitemid 351669587)
17. A. Sinner, N. Hasselmann, and P. Kopietz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.120601 102, 120601 (2009).
18. A. Sinner, N. Hasselmann, and P. Kopietz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.063632 82, 063632 (2010).
19. A. Rançon and N. Dupuis, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.172501 83, 172501 (2011).
20. J. K. Freericks and H. Monien, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/26/7/012 26, 545 (1994).
21. J. K. Freericks and H. Monien, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.53.2691 53, 2691 (1996).
22. J. K. Freericks, H. R. Krishnamurthy, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053631 79, 053631 (2009).
23. P. Buonsante and A. Vezzani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.013614 72, 013614 (2005). (Pubitemid 41492546)
24. F. E. A. dos Santos and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.013614 79, 013614 (2009).
25. N. Teichmann, D. Hinrichs, M. Holthaus, and A. Eckardt, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.100503 79, 100503 (2009).
26. N. Teichmann, D. Hinrichs, M. Holthaus, and A. Eckardt, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.224515 79, 224515 (2009).
27. W. Koller and N. Dupuis, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/18/41/019 18, 9525 (2006). (Pubitemid 44508556)
28. M. Knap, E. Arrigoni, and W. von der Linden, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.024301 81, 024301 (2010).
29. M. Knap, E. Arrigoni, and W. von der Linden, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.134507 83, 134507 (2011).
30. E. Arrigoni, M. Knap, and W. von der Linden, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.115145 84, 014535 (2011).
31. S. T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 417 (1958)
32. S. T. Beliaev, [Sov. Phys. JETP 7, 289 (1958)].
33. S. T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 433 (1958)
34. S. T. Beliaev, [Sov. Phys. JETP 7, 299 (1958)].
35. N. M. Hugenholtz and D. Pines, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.116.489 116, 489 (1959).
36. J. Gavoret and P. Nozières, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(64)90200-3 28, 349 (1964).
37. Y. A. Nepomnyashchii and A. A. Nepomnyashchii, Zh. Eksp. Teor. Fiz. 75, 976 (1978)
38. Y. A. Nepomnyashchii and A. A. Nepomnyashchii, [Sov. Phys. JETP 48, 493 (1978)].
39. Y. A. Nepomnyashchii, Zh. Eksp. Teor. Fiz 85, 1244 (1983)
40. Y. A. Nepomnyashchii, [Sov. Phys. JETP 58, 722 (1983)].
41. A. Z. Patasinskij and V. L. Pokrovskij, Zh. Eksp. Teor. Fiz. 64, 1445 (1973)
42. A. Z. Patasinskij and V. L. Pokrovskij, [Sov. Phys. JETP 37, 733 (1973)].
43. M. E. Fisher, M. N. Barber, and D. Jasnow, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.8.1111 8, 1111 (1973).
44. R. Anishetty, R. Basu, N. D. H. Dass, and H. S. Sharatchandra, Int. J. Mod. Phys. A IMPAEF 0217-751X 10.1142/S0217751X99001615 14, 3467 (1999).
45. S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.59.14054 59, 14054 (1999).
46. W. Zwerger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 027203 92, 027203 (2004).
47. N. Dupuis, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.031120 83, 031120 (2011).
48. A. A. Nepomnyashchii and Y. A. Nepomnyashchii, Pis'ma Zh. Eksp. Teor. Fiz. 21, 3 (1975)
49. A. A. Nepomnyashchii and Y. A. Nepomnyashchii, [JETP Lett. 21, 1 (1975)].
50. F. Pistolesi, C. Castellani, C. Di Castro, and G. C. Strinati, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.024513 69, 024513 (2004).
51. B. Capogrosso-Sansone, S. Giorgini, S. Pilati, L. Pollet, N. Prokof'ev, B. Svistunov, and M. Troyer, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/ 4/043010 12, 043010 (2010).
52. V. N. Popov, Theor. Math. Phys. (Sov.) 11, 236 (1972).
53. V. N. Popov and A. V. Seredniakov, Zh. Eksp. Teor. Fiz 77, 377 (1979)
54. V. N. Popov and A. V. Seredniakov, [Sov. Phys. JETP 50, 193 (1979)].
55. V. N. Popov, Functional Integrals and Collective Excitations (Cambridge University Press, Cambridge, England, 1987).
56. K. Sheshadri, H. R. Krishnamurthy, R. Pandit, and T. V. Ramakrishnan, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/22/4/004 22, 257 (1993).
57. D. van Oosten, P. van der Straten, and H. T. C. Stoof, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.053601 63, 053601 (2001).
58. K. Sengupta and N. Dupuis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.033629 71, 033629 (2005). (Pubitemid 40648534)
59. Y. Ohashi, M. Kitaura, and H. Matsumoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.033617 73, 033617 (2006).
60. C. Menotti and N. Trivedi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.235120 77, 235120 (2008).
61. C. Wetterich, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(93)90726-X 301, 90 (1993).
62. S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University, Cambridge, England, 2011).
63. J.-P. Blaizot, R. Méndez-Galain, and N. Wschebor, Phys. Lett. B PYLBAJ 0370-2693 10.1016/j.physletb.2005.10.086 632, 571 (2006). (Pubitemid 43006016)
64. F. Benitez, J. P. Blaizot, H. Chaté, B. Delamotte, R. Méndez-Galain, and N. Wschebor, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.030103 80, 030103 (R) (2009).
65. F. Benitez, R. Méndez-Galain, and N. Wschebor, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.024431 77, 024431 (2008).
66. For similar approximations in the classical O (N) model, see D. Guerra, R. Méndez-Galain, and N. Wschebor, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2007-00296-x 59, 357 (2007). (Pubitemid 350037079)
67. P. Anders, E. Gull, L. Pollet, M. Troyer, and P. Werner, New J. Phys. 10.1088/1367-2630/13/7/075013 13, 075013 (2011).
68. P. Anders, E. Gull, L. Pollet, M. Troyer, and P. Werner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.096402 105, 096402 (2010).
69. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.63.214503 63, 214503 (2001).
70. B. D. Josephson, Phys. Lett. PHLTAM 0031-9163 10.1016/0031-9163(66)90088- 6 21, 608 (1966).
71. D. S. Petrov, D. M. Gangardt, and G. V. Shlyapnikov, J. Phys. IV JPICEI 1155-4339 10.1051/jp4:2004116001 116, 5 (2004).
72. M. Schick, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.3.1067 3, 1067 (1971).
73. D. S. Fisher and P. C. Hohenberg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.37.4936 37, 4936 (1988).
74. A. Rançon and N. Dupuis, e-print arXiv: 1107.1314 (unpublished).
75. - 3 to the sound mode in two dimensions (see, e.g., A. Kreisel, F. Sauli, N. Hasselmann, and P. Kopietz, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.035127 78, 035127 (2008)). This damping makes the square-root singularity near ω = c | q | less visible but the continuum of excitations due to the singular longitudinal propagator remains visible away from ω = c | q |, in particular in the strongly correlated superfluid phase (see text).
76. S. D. Huber, E. Altman, H. P. Büchler, and G. Blatter, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.085106 75, 085106 (2007).
77. See, e.g., J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3rd ed. (Clarendon Press, Oxford, 1996).
78. See, for instance, Appendix G in R. B. Diener, R. Sensarma, and M. Randeria, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.023626 77, 023626 (2008). (Pubitemid 351391367)
79. D. Litim, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(00)00748-6 486, 92 (2000).