Abstract
We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. First we show that the Hamiltonian for an interaction which is long range in real space can be written as a quadratic from in bosons (bosonization) and calculate the spectral weight. For weak interactions the boundary exponent of the power-law suppression of the weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to investigate the spectral properties within the Hartree-Fock approximation. It gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained by using the density-matrix renormalization-group algorithm. Again many aspects of the behavior of the spectral function close to the boundary can be understood within the Hartree-Fock approximation. For the Hubbard model with weak interaction U the spectral weight is enhanced in a large energy range around the chemical potential. Following a crossover at exponentially (in 1/U) small energies a power-law suppression, as predicted by bosonization, sets in. This shows that for small U bosonization only holds on exponentially small energy scales.
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References
For a review see: J. Voit, Rep. Prog. Phys. 58, 977 (1995).
S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950).
J.M. Luttinger, J. Math. Phys. 4, 1154 (1963).
D.C. Mattis and E.H. Lieb, J. Math. Phys. 6, 304 (1965).
Here we do not consider umklapp scattering processes which only occur in lattice models and even there are irrelevant as long as the interaction is sufficient weak or the filling factor sufficient incommensurable (see e.g. Ref. [1]).
J. Sólyom, Adv. Phys. 28, 201 (1979).
F.D.M. Haldane, J. Phys. C14, 2585 (1981).
R. Preuss et al., Phys. Rev. Lett. 73, 732 (1994).
For a recent review of the experimental situation see: M. Grioni and J. Voit in Electron spectroscopies applied to low-dimensional materials, ed. by H. Stanberg and H. Hughes (1999).
D.C. Mattis, J. Math. Phys. 15, 609 (1974).
C.L. Kane and M.P.A. Fisher, Phys. Rev. Lett. 68, 1220 (1992).
M. Fabrizio and A. Gogolin, Phys. Rev. B 51, 17827 (1995).
S. Eggert et al., Phys. Rev. Lett. 76, 1505 (1996).
Y. Wang et al., Phys. Rev. B 54, 8491 (1996).
K. Schönhammer et al., Phys. Rev. B 61, 4393 (2000).
J. Voit et al., Phys. Rev. B 61, 7930 (2000).
V. Meden et al., cond-mat/0002215 and Eur. Phys. J. B (2000), in press.
The additional states are assumed to be filled in the ground state and thus do not modify the low-energy physics of the model.
This implies that for repulsive interactions (Ṽ (0) > 0) the prefactor of the logarithm in Eq. (9) is positive and the perturbative expression indicates a suppression of the weight.
Density-Matrix Renormalization, ed. by I. Peschel et al. (Springer, Berlin, 1999) and references therein.
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Meden, V., Metzner, W., Schollwöck, U., Schönhammer, K. (2001). Inhomogeneous Luttinger Liquids: Power-Laws and Energy Scales. In: Bonča, J., Prelovšek, P., Ramšak, A., Sarkar, S. (eds) Open Problems in Strongly Correlated Electron Systems. NATO Science Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0771-9_29
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DOI: https://doi.org/10.1007/978-94-010-0771-9_29
Publisher Name: Springer, Dordrecht
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