Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 1, 2008, Pages

  Deng, Xiaolong ^a   Citro, R ^a,b   Minguzzi, A ^a   Orignac, E ^c  

^a UNIVERSITÉ JOSEPH FOURIER   (France)

^b UNIVERSITY OF SALERNO   (Italy)

^c Laboratoire de Physique UMR CNRS ENSL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOSONS; GLASS; MOMENTUM; MOTT INSULATORS; PHASE DIAGRAMS; STATISTICAL MECHANICS;

DENSITY MATRIX RENORMALIZATION GROUP; INTERACTING BOSE GAS; LATTICE POTENTIALS; LUTTINGER LIQUIDS; MOMENTUM DISTRIBUTIONS; MOTT-INSULATING STATE; REPULSIVE INTERACTIONS; SHORT RANGE INTERACTIONS;

GLASS TRANSITION;

EID: 47749151908     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.013625     Document Type: Article

References (55)

1. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).
2. 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).
3. T. Giamarchi and H. J. Schulz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.37.325 37, 325 (1988).
4. M. H. W. Chan, K. I. Blum, S. Q. Murphy, G. K. S. Wong, and J. D. Reppy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.1950 61, 1950 (1988).
5. G. K. S. Wong, P. A. Crowell, H. A. Cho, and J. D. Reppy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.2410 65, 2410 (1990).
6. A. van Oudenaarden, S. J. K. Várdy, and J. E. Mooij, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4257 77, 4257 (1996).
7. W. Krauth, N. Trivedi, and D. Ceperley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.2307 67, 2307 (1991).
8. S. Zhang, N. Kawashima, J. Carlson, and J. E. Gubernatis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1500 74, 1500 (1995).
9. F. Alet and E. S. Sorensen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.024513 70, 024513 (2004).
10. P. Hitchcock and E. S. Sorensen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.174523 73, 174523 (2006).
11. I. M. Lifshitz, L. P. Pastur, and S. Gredeskul, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
12. N. F. Mott and A. D. Twose, Adv. Phys. ADPHAH 0001-8732 10.1080/00018736100101271 10, 107 (1961).
13. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004).
14. S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69. 2863 69, 2863 (1992)
15. S. R. White, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.10345 48, 10345 (1993).
16. U. Schollwöck, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 77.259 77, 259 (2005).
17. G. G. Batrouni and R. T. Scalettar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.9051 46, 9051 (1992).
18. B. V. Svistunov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.16131 54, 16131 (1996)
19. N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.4355 80, 4355 (1998).
20. J. K. Freericks and H. Monien, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.2691 53, 2691 (1996).
21. P. Schmitteckert, T. Schulze, C. Schuster, P. Schwab, and U. Eckern, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.560 80, 560 (1998).
22. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/415039a 415, 39 (2002).
23. L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.130404 98, 130404 (2007).
24. J. E. Lye, L. Fallani, C. Fort, V. Guarrera, M. Modugno, D. S. Wiersma, and M. Inguscio, e-print arXiv:cond-mat/0611146.
25. P. G. Harper, Proc. Phys. Soc., London, Sect. A PPSAAM 0370-1298 10.1088/0370-1298/68/10/304 68, 874 (1955)
26. S. Aubry, in Solitons and Condensed Matter Physics, edited by, A. R. Bishop, and, T. Schneider, (Springer, New York, 1978)
27. S. Aubry and G. Andre, Ann. Isr. Phys. Soc. AIPSDK 0309-8710 3, 133 (1980)
28. S. Aubry, J. Phys. (Paris) JOPQAG 0302-0738 10.1051/jphys: 01983004402014700 44, 147 (1983).
29. D. R. Hofstadter, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.14.2239 14, 2239 (1976).
30. Ya. Svetlana Jitomirskaya, Ann. Math. ANMAAH 0003-486X 10.2307/121066 150, 1159 (1999).
31. M. Girardeau, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703687 1, 516 (1960)
32. M. D. Girardeau, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.139.B500 139, B500 (1965).
33. A. M. Rey, I. I. Satija, and C. W. Clark, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.063610 73, 063610 (2006).
34. C. Schuster, R. A. Romer, and M. Schreiber, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.115114 65, 115114 (2002).
35. T. D. Kühner and H. Monien, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.R14741 58, R14741 (1998).
36. V. A. Kashurnikov and B. V. Svistunov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.11776 53, 11776 (1996).
37. R. Roth and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.023604 68, 023604 (2003).
38. T. Roscilde, e-print arXiv:0712.2741.
39. H. P. Büchler, G. Blatter, and W. Zwerger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.130401 90, 130401 (2003).
40. 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).
41. In the definition of the Harper model, α is an irrational number. However, to all practical purposes and in numerical calculations it is then approximated by a close rational number.
42. J. X. Zhong and R. Mosseri, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/7/44/008 7, 8383 (1995).
43. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 47.1840 47, 1840 (1981).
44. M. Cazalilla, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/37/7/051 37, S1 (2004).
45. G. I. Dzhaparidze and A. A. Nersesyan, JETP Lett. 27, 334 (1978). 0021-3640
46. H. J. Schulz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.22.5274 22, 5274 (1980).
47. J. Vidal, D. Mouhanna, and T. Giamarchi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3908 83, 3908 (1999).
48. J. Vidal, D. Mouhanna, and T. Giamarchi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.014201 65, 014201 (2001).
49. S. Rapsch, U. Schollwöck, and W. Zwerger, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1999-00302-7 46, 559 (1999)
50. L. Urba and R. P. Anders, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.104406 67, 104406 (2003).
51. N. Hatano, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.64.1529 64, 1529 (1995).
52. J. C. Slater, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.87.807 87, 807 (1952).
53. M. Krämer, C. Menotti, L. Pitaevskii and S. Stringari, Eur. Phys. J. D EPJDF6 1434-6060 10.1140/epjd/e2003-00284-4 27, 247 (2003).
54. By following Ref., it can be shown that the functions φ0 (1) satisfy Bloch's theorem and give rise to bands, thus an equation equivalent to Eq. 13 can be derived also for weakly interacting bosons.
55. G. Roux, e-print arXiv:0802.3774.