Abstract.
An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Dzyaloshinskii, Phys. Rev. B 68, 85113 (2003)
F.H.L. Essler, A.M. Tsvelik, Phys. Rev. B 65, 115117 (2002); F.H.L. Essler, A.M. Tsvelik, Phys. Rev. B 71, 195116 (2005)
R.M. Konik, T.M. Rice, A.M. Tsvelik, Phys. Rev. Lett. 96, 086407 (2006)
K.-Y. Yang, T.M. Rice, F.-C. Zhang, Phys. Rev. B 73, 174501(2006)
T.D. Stanescu, P.W. Phillips, T-P. Choy, Phys. Rev. B 75, 104503 (2007)
C. Berthod, T. Giarmarchi, S. Biermann, A. Georges, Phys. Rev. Lett. 97, 136401 (2006)
J. Ortloff, M. Balzer, M. Potthoff, Eur. Phys. J. B 58, (2007) 37.
J. M Luttinger, Phys. Rev. 119, 1153 (1960); J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960)
S. Trebst, H. Monien, A. Grzesik, M. Sigrist, Phys. Rev. B 73, 165101 (2006)
J. Hubbard, Proc. R. Soc. (London), Ser. A 276, 238 (1963)
W. Jones, N.H. March, Theoretical Solid State Physics, Vol. 1 (John Wiley & Sons, London, 1973)
S. Pairault, D. Sénéchal, A.-M.S. Tremblay, Phys. Rev. Lett. 80, 5389 (1998)
M. Potthoff, Condens. Mat. Phys. 9, 557 (2006)
B.L. Altshuler, A.V. Chubukov, A. Dashevskii, A.M. Finkel'stein, D.K. Morr, Europhys. Lett. 41, 401 (1998)
The non-analytic kinks in Figure 2 are a trivial artifact of the non-analytic dependence of the bare coupling constants on λ. They do therefore not signal a quantum phase transition
G. Moeller, V. Dobrosavljević, A.E. Ruckenstein, Phys. Rev. B 59, 6846 (1999); A. Fuhrmann, D. Heilmann, H. Monien, Phys. Rev. B 73, 245118 (2006)
T. Senthil, S. Sachdev, M. Vojta, Phys. Rev. Lett. 90, 216403 (2003)
M. Oshikawa, Phys. Rev. Lett. 84, 3370 (2000)
A. Praz, J. Feldman, H. Knörrer, E. Trubowitz, Europhys. Lett. 72, 49 (2005)
M. Langer, J. Schmalian, S. Grabowski, K.H. Bennemann, Phys. Rev. Lett. 75, 4508 (1995); C. Grober, R. Eder, W. Hanke, Phys. Rev. B 62, 4336 (2000); K. Haule, A. Rosch, J. Kroha, P. Wölfle, Phys. Rev. Lett. 89, 236402 (2002); Phys. Rev. B 68, 155119 (2003)
Y.M. Vlik, A.-M.S. Tremblay, J. Phys. I France. 7, 1309 (1997)
J. Kokalj, P. Prelovsek, Phys. Rev. B 75, 045111 (2007)
N. Nagaosa, J. Takimoto, J. Phys. Soc. Jpn 55, 2735 (1986)
M. Fabrizio, A.O. Gogolin, A.A. Nersesyan, Phys. Rev. Lett. 83, 2014 (1999)
N. Paris, K. Bouadim, F. Hebert, G.G. Batrouni, R.T. Scalettar, Phys. Rev. Lett. 98, 046403 (2007)
M.E. Torio, A.A. Aligia, G.I. Japaridze, B. Normand, Phys. Rev. B 73, 115109 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rosch, A. Breakdown of Luttinger's theorem in two-orbital Mott insulators . Eur. Phys. J. B 59, 495–502 (2007). https://doi.org/10.1140/epjb/e2007-00312-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2007-00312-3