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
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.
PACS: 71.10.-w – Theories and models of many electron systems / 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000