Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $K_{\rho}$ and
$v_{\sigma}$. 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 $K_{\rho}$ are in good agreement with weak-coupling perturbative
estimates $K_{\rho}^{pert}$ at high densities, but deviate strongly at low
densities, especially when the electron-electron interaction is screened at
long distances. $K_{\rho}^{pert}\sim n^{1/2}$ vanishes at small carrier density
$n$ whereas we conjecture that $K_{\rho}\to 1/2$ when $n\to 0$, implying that
$K_{\rho}$ 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 $n$. Strong correlation effects make it difficult to obtain fully
consistent estimates of $v_{\sigma}$ from Hartree-Fock calculations. We
conjecture that $v_{\sigma}/\vf\propto n/V_0$ in the limit $n\to 0$ where $V_0$
is the interaction strength.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph