77 research outputs found
Parity effect in a mesoscopic Fermi gas
We develop a quantitative analytic theory that accurately describes the
odd-even effect observed experimentally in a one-dimensional, trapped Fermi gas
with a small number of particles [G. Z\"urn et al., Phys. Rev. Lett. 111,
175302 (2013)]. We find that the underlying physics is similar to the parity
effect known to exist in ultrasmall mesoscopic superconducting grains and
atomic nuclei. However, in contrast to superconducting nanograins, the density
(Hartree) correction dominates over the superconducting pairing fluctuations
and leads to a much more pronounced odd-even effect in the mesoscopic, trapped
Fermi gas. We calculate the corresponding parity parameter and separation
energy using both perturbation theory and a path integral framework in the
mesoscopic limit, generalized to account for the effects of the trap, pairing
fluctuations, and Hartree corrections. Our results are in an excellent
quantitative agreement with experimental data and exact diagonalization.
Finally, we discuss a few-to-many particle crossover between the perturbative
mesoscopic regime and non-perturbative many-body physics that the system
approaches in the thermodynamic limit.Comment: 7 pages, 1 figur
Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator
Topological Kondo insulators are strongly correlated materials, where
itinerant electrons hybridize with localized spins giving rise to a
topologically non-trivial band structure. Here we use non-perturbative
bosonization and renormalization group techniques to study theoretically a
one-dimensional topological Kondo insulator. It is described as a
Kondo-Heisenberg model where the Heisenberg spin-1/2 chain is coupled to a
Hubbard chain through a Kondo exchange interaction in the p-wave channel - a
strongly correlated version of the prototypical Tamm-Shockley model. We derive
and solve renormalization group equations at two-loop order in the Kondo
parameter, and find that, at half-filling, the charge degrees of freedom in the
Hubbard chain acquire a Mott gap, even in the case of a non-interacting
conduction band (Hubbard parameter ). Furthermore, at low enough
temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic
interactions along the rungs, effectively locking the spin degrees of freedom
into a spin- chain with frozen charge degrees of freedom. This structure
behaves as a spin-1 Haldane chain, a prototypical interacting topological spin
model, and features two magnetic spin- end states for chains with open
boundary conditions. Our analysis allows to derive an insightful connection
between topological Kondo insulators in one spatial dimension and the
well-known physics of the Haldane chain, showing that the ground state of the
former is qualitatively different from the predictions of the naive mean-field
theory.Comment: 13 pages, 2 figures, 1 appendix. New version with typos correcte
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