Abstract
We derive an effective field theory describing the long wavelength, low energy properties of one-dimensional (1D) attractive Fermi gases with spin imbalance. Our theory is based on the exact solution (Bethe ansatz) of the microscopic Hamiltonian, the Gaudin-Yang model. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a novel quantum fluid, a two-component Luttinger liquid with spin-charge mixing. Applying the theory, we obtain the correlation functions and the universal low temperature thermodynamics. Our theory can also predict the phase diagram of weakly coupled 1D gases, a quasi-1D system recently realized in experiments at Rice university.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G.B. Partridge, W. Li, R.I. Kamar, Y.-A. Liao, R.G. Hulet, Science 311, 503 (2006)
M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006)
M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle, Nature 442, 54 (2006)
Y. Shin, M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle, Phys. Rev. Lett. 97, 030401 (2006)
G.B. Partridge, W. Li, Y.A. Liao, R.G. Hulet, M. Haque, H.T.C. Stoof, Phys. Rev. Lett. 97, 190407 (2006)
C.H. Schunck, Y. Shin, A. Schirotzek, M.W. Zwierlein, W. Ketterle, Science 316, 867 (2007)
R. Casalbuoni, G. Nardulli, Rev. Mod. Phys. 76, 263 (2004)
D.E. Sheehy, L. Radzihovsky, Ann. Phys. 322, 1790 (2007) and references therein
K. Yang, Phys. Rev. B 63, 140511(R) (2001)
M.M. Parish, S.K. Baur, E.J. Mueller, D.A. Huse, Phys. Rev. Lett. 99, 250403 (2007)
E. Zhao, W.V. Liu, Phys. Rev. A 78, 063605 (2008)
M. Gaudin, Phys. Lett. A 24, 55 (1967)
C.N. Yang, Phys. Rev. Lett. 19, 1312 (1967)
G. Orso, Phys. Rev. Lett. 98, 070402 (2007)
H. Hu, X.-J. Liu, P.D. Drummond, Phys. Rev. Lett. 98, 070403 (2007)
H. Hu, X.-J. Liu, P.D. Drummond, Phys. Rev. A 76, 043605 (2007)
X.W. Guan et al., Phys. Rev. B 76, 085120 (2007)
F.D.M. Haldane, J. Phys. A 15, 507 (1982)
A. Lüscher, R.M. Noack, A.M. Läuchli, Phys. Rev. A 78, 013637 (2008)
A.E. Feiguin, F. Heidrich-Meisner, Phys. Rev. B 76, 220508(R) (2007)
M. Tezuka, M. Ueda, Phys. Rev. Lett. 100, 110403 (2008)
M. Rizzi, M. Polini, M.A. Cazalilla, M.R. Bakhtiari, M.P. Tosi, R. Fazio, Phys. Rev. B 77, 245105 (2008)
F.H.L. Essler, H. Frahm, F. Göhmann, A. Klümper, V.E. Korepin, The One-dimensional Hubbard Model (Cambridge University Press, Cambridge, 2005)
V.J. Emery, Phys. Rev. B 14, 2989 (1976)
H. Frahm, V.E. Korepin, Phys. Rev. B 10, 553 (1990)
H. Frahm, V.E. Korepin, Phys. Rev. B 43, 5653 (1991)
K. Penc, J. Sólyom, Phys. Rev. B 47, 6273 (1993)
K.-V. Pham, M. Gabay, P. Lederer, Phys. Rev. B 61, 16397 (2000)
H. Frahm, T. Vekua, J. Stat. Mech. (2008). doi:10.1088/1742-5468/2008/01/P01007
T. Hikihara, A. Furusaki, K.A. Matveev, Phys. Rev. B 72, 035301 (2005)
H.W. Blöte, J.L. Cardy, M.P. Nightingale, Phys. Rev. Lett. 56, 742 (1986)
I. Affleck, Phys. Rev. Lett. 56, 746 (1986)
P. Kakashvili, C.J. Bolech, Phys. Rev. A 79, 041603 (2009)
M. Casula, D.M. Ceperley, E.J. Mueller, Phys. Rev. A 78, 033607 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, E., Liu, W.V. An Effective Field Theory for One-dimensional Polarized Fermi Gases. J Low Temp Phys 158, 36–42 (2010). https://doi.org/10.1007/s10909-009-9948-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-009-9948-1