3 research outputs found
Ladder approximation to spin velocities in quantum wires
The spin sector of charge-spin separated single mode quantum wires is
studied, accounting for realistic microscopic electron-electron interactions.
We utilize the ladder approximation (LA) to the interaction vertex and exploit
thermodynamic relations to obtain spin velocities. Down to not too small
carrier densities our results compare well with existing quantum Monte-Carlo
(QMC) data. Analyzing second order diagrams we identify logarithmically
divergent contributions as crucial which the LA includes but which are missed,
for example, by the self-consistent Hartree-Fock approximation. Contrary to
other approximations the LA yields a non-trivial spin conductance. Its
considerably smaller computational effort compared to numerically exact
methods, such as the QMC method, enables us to study overall dependences on
interaction parameters. We identify the short distance part of the interaction
to govern spin sector properties.Comment: 6 pages, 6 figures, to appear in Physical Review
Tomonaga-Luttinger parameters for quantum wires
The low-energy properties of a homogeneous one-dimensional electron system
are completely specified by two Tomonaga-Luttinger parameters and
. In this paper we discuss microscopic estimates of the values of
these parameters in semiconductor quantum wires that exploit their relationship
to thermodynamic properties. Motivated by the recognized similarity between
correlations in the ground state of a one-dimensional electron liquid and
correlations in a Wigner crystal, we evaluate these thermodynamic quantities in
a self-consistent Hartree-Fock approximation. According to our calculations,
the Hartree-Fock approximation ground state is a Wigner crystal at all electron
densities and has antiferromagnetic order that gradually evolves from
spin-density-wave to localized in character as the density is lowered. Our
results for are in good agreement with weak-coupling perturbative
estimates at high densities, but deviate strongly at low
densities, especially when the electron-electron interaction is screened at
long distances. vanishes at small carrier density
whereas we conjecture that when , implying that
should pass through a minimum at an intermediate density.
Observation of such a non-monotonic dependence on particle density would allow
to measure the range of the microscopic interaction. In the spin sector we find
that the spin velocity decreases with increasing interaction strength or
decreasing . Strong correlation effects make it difficult to obtain fully
consistent estimates of from Hartree-Fock calculations. We
conjecture that v_{\sigma}/\vf\propto n/V_0 in the limit where
is the interaction strength.Comment: RevTeX, 23 pages, 8 figures include