Eur. Phys. J. B 16, 631-646 (2000)
https://doi.org/10.1007/s100510070180

Luttinger liquids with boundaries: Power-laws and energy scales

¹ Institut für Theoretische Physik C, RWTH Aachen, 52056 Aachen, Germany
² Institut für Theoretische Physik, Universität Göttingen, Bunsenstrasse 9, 37073 Göttingen, Germany
³ Sektion Physik, Universität München, Theresienstrasse 37, 80333 München, Germany

Received: 8 February 2000
Revised: 25 April 2000
Published online: 15 August 2000

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 ) 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.