Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

Physical Review B - Condensed Matter and Materials Physics

Volumn 77, Issue 23, 2008, Pages

  Byczuk, Krzysztof ^a,b   Vollhardt, Dieter ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 45249105720     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.235106     Document Type: Article

References (60)

1. R. J. Anglin and W. Ketterle, Nature (London) NATUAS 0028-0836 10.1038/416211a 416, 211 (2002).
2. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/415039a 415, 39 (2002).
3. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730701223200 56, 243 (2007).
4. I. Bloch, J. Dalibard, and W. Zwerger, arXiv:0704.3011, Rev. Mod. Phys. (to be published).
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. A. Isacsson, M.-Ch. Cha, K. Sengupta, and S. M. Girvin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.184507 72, 184507 (2005).
7. S. D. Huber, E. Altman, H. P. Büchler, and G. Blatter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.085106 75, 085106 (2007).
8. S. Sachdev, K. Sengupta, and S. M. Girvin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.075128 66, 075128 (2002).
9. A. Micheli, G. K. Brennen, and P. Zoller, Nat. Phys. ZZZZZZ 1745-2473 2, 341 (2006).
10. T. Matsubara and H. Matsuda, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.16.569 16, 569 (1956).
11. T. Matsubara and H. Matsuda, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.17.19 17, 19 (1957).
12. T. Morita, Prog. Theor. Phys. 18, 462 (1957). 0033-068X
13. 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).
14. G. G. Batrouni, R. T. Scalettar, and G. T. Zimanyi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.1765 65, 1765 (1990).
15. D. S. Rokhsar and B. G. Kotliar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.44.10328 44, 10328 (1991).
16. 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).
17. J. K. Freericks and H. Monien, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/26/7/012 26, 545 (1994).
18. J. K. Freericks and H. Monien, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.2691 53, 2691 (1996).
19. J. D. Reppy, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00114905 87, 205 (1992).
20. A. P. Kampf and G. T. Zimanyi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.279 47, 279 (1993).
21. C. Bruder, R. Fazio, and G. Schön, Ann. Phys. (Leipzig) APNYA6 0003-4916 14, 566 (2005).
22. T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5868 84, 5868 (2000)
23. Ch. Rüegg, N. Cavadini, A. Furrer, H.-U. Güdel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Nature (London) NATUAS 0028-0836 10.1038/nature01617 423, 62 (2003).
24. T. Giamarchi, Ch. Rüegg, and O. Tchernyshyov, Nat. Phys. ZZZZZZ 1745-2473 4, 198 (2008).
25. E. Kim and M. H. W. Chan, Nature (London) NATUAS 0028-0836 10.1038/nature02220 427, 225 (2004).
26. A. J. Leggett, Quantum Liquids (Oxford University Press, New York, 2006).
27. W. Metzner and D. Vollhardt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.324 62, 324 (1989).
28. Th. Pruschke, M. Jarrell, and J. K. Freericks, Adv. Phys. ADPHAH 0001-8732 10.1080/00018739500101526 44, 187 (1995).
29. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.13 68, 13 (1996).
30. G. Kotliar and D. Vollhardt, Phys. Today 57 (3), 53 (2004). 0031-9228
31. H. A. Gersch and G. C. Knollman, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.129.959 129, 959 (1963).
32. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.865 78, 865 (2006).
33. C. Itzykson and J.-M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1989), Vols. I and II.
34. E. Müller-Hartmann, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01311397 74, 507 (1989).
35. Q. Si and J. L. Smith, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3391 77, 3391 (1996).
36. H. Shi and A. Griffin, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98) 00015-5 304, 1 (1998).
37. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963).
38. L. Erdos, B. Schlein, and H.-T. Yau, Commun. Pure Appl. Math. CPMAMV 0010-3640 10.1002/cpa.20123 59, 1659 (2006).
39. L. Erdos, B. Schlein, and H.-T. Yau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.040404 98, 040404 (2007).
40. D. H. Kobe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.5.854 5, 854 (1972).
41. S. Stenholm, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.2942 57, 2942 (1998).
42. J.-B. Bru and T. C. Dorlas, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1025774821712 113, 177 (2003).
43. P. van Dongen and D. Vollhardt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.7252 40, 7252 (1989).
44. W. Krauth, M. Caffarel, and J.-Ph. Bouchaud, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.3137 45, 3137 (1992).
45. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).
46. E. Altman, W. Hofstetter, E. Demler, and M. D. Lukin, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/113 5, 113 (2003).
47. I. Titvinidze, M. Snoek, and W. Hofstetter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.100401 100, 100401 (2008).
48. J. K. Freericks and V. Zlatić, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.1333 75, 1333 (2003).
49. C. Ates and K. Ziegler, Phys. Rev. A. 71, 063610 (2005). 0034-7043
50. M. M. Maska, R. Lemanski, J. K. Freericks, and C. J. Williams, arXiv:0802.3894 (unpublished).
51. P. A. Martin and J. Piasecki, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.016113 68, 016113 (2003)
52. P. A. Martin and J. Piasecki, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.016109 71, 016109 (2005).
53. A quantum-mechanical system of noninteracting particles, which is coupled to a single site ("impurity"), where interactions are possible defines a so-called quantum-mechanical "single-impurity problem." In particular, the "bosonic single-impurity problem" discussed here requires the calculation of the local Green's function [Eq. 9] with an arbitrary local action [Eq. 10].
54. H.-J. Lee and R. Bulla, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2007-00118-3 56, 199 (2007).
55. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Menlo Park, 1988).
56. G. Rickayzen, Green's Functions and Condensed Matter (Academic, London, 1984).
57. M. Eckstein, M. Kollar, K. Byczuk, and D. Vollhardt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.235119 71, 235119 (2005).
58. M. Kollar, M. Eckstein, K. Byczuk, N. Blümer, P. van Dongen, M. H. Radke de Cuba, W. Metzner, D. Tanaskovic, V. Dobrosavljevic, G. Kotliar, and D. Vollhardt, Ann. Phys. (Leipzig) APNYA6 0003-4916 14, 642 (2005).
59. M. van den Berg, T. C. Dorlas, and V. B. Priezzhev, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01053795 69, 307 (1992).
60. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).