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Luttinger liquids with boundaries: Power-laws and energy scales

V. Meden·W. Metzner·U. Schollwoeck·O. Schneider·T. Stauber·K. Schoenhammer
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Abstract

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already 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 using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models.

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V. Meden, W. Metzner, U. Schollwoeck, O. Schneider, T. Stauber, K. Schoenhammer. 2000-02-15. Luttinger liquids with boundaries: Power-laws and energy scales. https://doi.org/10.1007/s100510070180

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