Münster 1999 – scientific programme
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TT: Tiefe Temperaturen
TT 18: Korrelierte Elektronensysteme (Theorie)
TT 18.6: Talk
Thursday, March 25, 1999, 11:15–11:30, F3
Dimensional crossover von einer zu unendlich vielen Dimensionen: von der Luttinger zur Fermi-Flüssigkeit? — •E. Arrigoni — Institut für Theoretische Physik Universität Würzburg, D-97074 Würzburg
It is well known that the Luttinger liquid state is unstable with respect to a small interliquid hopping t⊥ [1]. However, the fate of the final low-energy state is still unknown. Eventually, the isotropic system (t⊥∼ EF) is expected to become a Fermi liquid, but how the crossover between the two universality classes takes place is still a puzzle. A linked-cluster expansion in t⊥, although predicting the correct power-law behavior for static quantities as a function of t⊥ [2], is not sufficient to characterize the low-energy state even for arbitrarily small t⊥. Indeed, higher terms in the expansion diverge for energies smaller than t⊥, due to the relevance of the hopping. In this work, we show how these divergences can be resummed by renormalizing the propagator and the multi-legs vertices (cumulants) of the expansion. Here, we consider the crossover from one to infinite dimensions and carry out the vertices renormalization up to logarithmic accuracy in the small energy, in the same spirit as the renormalization group or parquet approach [3]. We discuss the new phase into which the perturbed Luttinger liquid flows for energies smaller than t⊥.
[1] C. Castellani, C. Di Castro, and W. Metzner, Phys. Rev. Lett. 69, 1703 (1992)
[2] E. Arrigoni, Phys. Rev. Lett. 80, 790 (98); S. Capponi, D. Poilblanc, E. Arrigoni, Phys. Rev. B 57, 6360, (98)
[3] B. Roulet and J. Gavoret and P. Nozières, Phys. Rev. 178, 1072 (69); Yu. A. Bychkov and L. P. Gor’kov and I. E. Dzyaloshinskii, Sov. Phys. JETP 23, 489 (66)