Universal short-distance structure of the single-particle spectral function of dilute Fermi gases

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 2, 2010, Pages

  Schneider, William ^a   Randeria, Mohit ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DILUTE FERMI GAS; HARD-SPHERE GAS; INTERACTION EFFECT; MOMENTUM DISTRIBUTIONS; SINGLE-PARTICLE SPECTRAL FUNCTION; SPECTRAL FUNCTION; SPECTRAL WEIGHT; UNITARITY; UNIVERSAL STRUCTURES;

ELECTRON GAS; FERMIONS; SPECTROSCOPY;

GASES;

EID: 76249092455     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.021601     Document Type: Article

References (38)

1. A. A. Abrikosov, L. P. Gorkov, and I. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963).
2. L. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, Elmsford, NY, 1962).
3. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
4. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.1215 80, 1215 (2008).
5. J. T. Stewart, J. P. Gaebler, and D. S. Jin, Nature (London) NATUAS 0028-0836 10.1038/nature07172 454, 744 (2008);
6. D. S. Jin (private communication).
7. C. Chin, Science SCIEAS 0036-8075 10.1126/science.1100818 305, 1128 (2004).
8. A. Schirotzek, Y. I. Shin, C. H. Schunck, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.140403 101, 140403 (2008).
9. A. Schirotzek, C. H. Wu, A. Sommer, and M. W. Zwierlein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.230402 102, 230402 (2009).
10. S. Tan, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2008.03.004 323, 2952 (2008);
11. S. Tan, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2008.03.005 323, 2971 (2008);
12. S. Tan, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2008.03.003 323, 2987 (2008).
13. E. Braaten and L. Platter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.205301 100, 205301 (2008);
14. F. Werner, L. Tarruell, and Y. Castin, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2009-00040-8 68, 401 (2009);
15. S. Zhang and A. J. Leggett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.023601 79, 023601 (2009).
16. M. Randeria, in Proceedings of the International School of Physics "Enrico Fermi," Course CXXXVI on High Temperature Superconductivity, edited by, G. Iadonisi., J. R. Schrieffer. and, M. L. Chiafalo, (IOS Press, Amsterdam, 1998);
17. M. Randeria, e-print arXiv: cond-mat/9710223.
18. V. A. Belyakov, Sov. Phys. JETP 13, 850 (1961). Note that Ref. [1] has a typographical error in the last equation of (5.24): the prefactor of k-4 is too large by a factor of 4.
19. For a hard-sphere gas, a=r0, the range, and the "large"-k regime where n(k)~k-4 is kF k 1/r0. Thus, unlike Ref. [9], where a r0, we cannot set r0=0.
20. We use μ=εF in L and G0 since the corrections to μ are of order kFa. This is also done for the large-N calculation for the polarized Fermi gas below.
21. P. Nikolic and S. Sachdev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.033608 75, 033608 (2007).
22. The simplification Γ g+g2L for the hard sphere gas is valid only for ω 1/ma2. ImΣ grows indefinitely for larger ω. We subtract out this singular behavior S(z)=-i(22/3π)(kFa)2εFz and then the Kramers-Kronig transform ImΣ=ImΣ-ImS. The real self-energy is then ReΣ=ReΣ +ReS.
23. We have checked our numerics against known results [1] for chemical potential μ, quasiparticle residue Z, effective mass m*, and the scattering rate near the Fermi surface.
24. Here a r0 and we set the range r0=0.
25. C. Lobo, A. Recati, S. Giorgini, and S. Stringari, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.200403 97, 200403 (2006);
26. R. Combescot, A. Recati, C. Lobo, and F. Chevy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.180402 98, 180402 (2007);
27. S. Pilati and S. Giorgini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.030401 100, 030401 (2008).
28. M. Veillette, E. G. Moon, A. Lamacraft, L. Radzihovsky, S. Sachdev, and D. E. Sheehy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.033614 78, 033614 (2008);
29. M. Veillette, D. Sheehy, and L. Radzihovsky, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.043614 75, 043614 (2007).
30. We have obtained more stringent bounds for the imbalanced case, using the detailed structure of ImΓ, but the simpler analysis described here suffices to establish a range linear in k centered about -ε(k).
31. R. Haussmann, M. Punk, and W. Zwerger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.063612 80, 063612 (2009).
32. R. B. Diener, R. Sensarma, and M. Randeria, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.023626 77, 023626 (2008);
33. see Sec. VI and especially Eq. (34).
34. A. Perali, P. Pieri, and G. C. Strinati, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.010402 100, 010402 (2008).
35. Our result here corrects a factor of 2 in W. Schneider, V. Shenoy, and M. Randeria, e-print arXiv: 0903.3006 [cond-mat].
36. This large-ω tail is valid for εF ω 1/ma'2≤1/mr02, where a' characterizes the final state interactions and r0 is the range.
37. P. Pieri, A. Perali, and G. C. Strinati, Nature Phys. PRLTAO 1745-2473 10.1038/nphys1345 5, 736 (2009), attribute the coefficient Δ ∞ pairing fluctuations above Tc. Our results, however, show that this universal tail is related to the "contact" and not necessarily to pairing, either above or below Tc.
38. R. Combescot, F. Alzetto, and X. Leyronas, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053640 79, 053640 (2009).