Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2004-02-03
J. Phys. B: At. Mol. Opt. Phys. 37, 2363-2377(2004)
Physics
Condensed Matter
Strongly Correlated Electrons
20 pages, minor changes, typos and journal-ref added
Scientific paper
10.1088/0953-4075/37/11/013
A phase operator formulation for a recent model of interacting one-dimensional fermions in a harmonic trap is developed. The resulting theory is similar to the corresponding approach for the Luttinger model with open boundary conditions (OBC). However, in place of the spatial coordinate $z$, a dimensionless variable $u$ defined on the unit circle appears as argument of the phase fields and $u$ is non-linearly related to $z$. Furthermore, form factors appear which reflect the harmonic trap geometry. The theory is applied to calculate one-particle correlation functions. In a properly defined thermodynamic limit, bulk and boundary critical exponents are calculated for the static two-point correlation function and the dynamic local correlation function. The local spectral density is also considered. The critical exponents found are in agreement with those known for OBC with the exception of the boundary scaling exponent $\Delta_\perp$.
Wonneberger W.
Xianlong Gao
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