7,581 research outputs found
High density limit of the two-dimensional electron liquid with Rashba spin-orbit coupling
We discuss by analytic means the theory of the high-density limit of the
unpolarized two-dimensional electron liquid in the presence of Rashba or
Dresselhaus spin-orbit coupling. A generalization of the ring-diagram expansion
is performed. We find that in this regime the spin-orbit coupling leads to
small changes of the exchange and correlation energy contributions, while
modifying also, via repopulation of the momentum states, the noninteracting
energy. As a result, the leading corrections to the chirality and total energy
of the system stem from the Hartree-Fock contributions. The final results are
found to be vanishing to lowest order in the spin-orbit coupling, in agreement
with a general property valid to every order in the electron-electron
interaction. We also show that recent quantum Monte Carlo data in the presence
of Rashba spin-orbit coupling are well understood by neglecting corrections to
the exchange-correlation energy, even at low density values.Comment: 11 pages, 5 figure
Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions
We discuss a general form of the exchange energy for a homogeneous system of
interacting electrons in two spatial dimensions which is particularly suited in
the presence of a generic spin-orbit interaction. The theory is best formulated
in terms of a generalized fractional electronic polarization. Remarkably we
find that a net generalized polarization does not necessarily translate into an
increase in the magnitude of the exchange energy, a fact that in turn favors
unpolarized states. Our results account qualitatively for the findings of
recent experimental investigations
Correlation energy in a spin polarized two dimensional electron liquid in the high density limit
We have obtained an analytic expression for the ring diagrams contribution to
the correlation energy of a two dimensional electron liquid as a function of
the uniform fractional spin polarization. Our results can be used to improve on
the interpolation formulas which represent the basic ingredient for the
constructions of modern spin-density functionals in two dimensions.Comment: 3 pages, 1 figur
Two exact properties of the perturbative expansion for the two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit coupling
We have identified two useful exact properties of the perturbative expansion
for the case of a two-dimensional electron liquid with Rashba or Dresselhaus
spin-orbit interaction and in the absence of magnetic field. The results allow
us to draw interesting conclusions regarding the dependence of the exchange and
correlation energy and of the quasiparticle properties on the strength of the
spin-orbit coupling which are valid to all orders in the electron-electron
interaction.Comment: 6 pages, 1 figur
Universal finite size corrections and the central charge in non solvable Ising models
We investigate a non solvable two-dimensional ferromagnetic Ising model with
nearest neighbor plus weak finite range interactions of strength \lambda. We
rigorously establish one of the predictions of Conformal Field Theory (CFT),
namely the fact that at the critical temperature the finite size corrections to
the free energy are universal, in the sense that they are exactly independent
of the interaction. The corresponding central charge, defined in terms of the
coefficient of the first subleading term to the free energy, as proposed by
Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all
0<\lambda<\lambda_0 and \lambda_0 a small but finite convergence radius. This
is one of the very few cases where the predictions of CFT can be rigorously
verified starting from a microscopic non solvable statistical model. The proof
uses a combination of rigorous renormalization group methods with a novel
partition function inequality, valid for ferromagnetic interactions.Comment: 43 pages, 1 figur
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