12,841 research outputs found
Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillings
Get PDFWe show that a Hopf term exists in the effective action of long-wavelength
skyrmions in quantum Hall systems for both odd integer and fractional filling
factors , where is an integer. We evaluate the prefactor
of the Hopf term using Green function method in the limit of strong external
magnetic field using model of local interaction. The prefactor () of the
Hopf term is found to be equal to . The spin and charge densities and
hence the total spin and charge of the skyrmion are computed from the effective
action. The total spin is found to have a dominant contribution from the Berry
term in the effective action and to increase with the size of the skyrmion. The
charge and the statistics of the skyrmion, on the other hand, are completely
determined by the prefactor of the Hopf term. Consequently, the skyrmions have
charge and are Fermions (anyons) for odd integer (fractional) fillings.
We also obtain the effective action of the skyrmions at finite temperature. It
is shown that at finite temperature, the value of the prefactor of the Hopf
term depends on the order in which the zero-momentum and zero-frequency limits
are taken.Comment: Replaced with revised versio
Non-equilibrium phonon dynamics in trapped ion systems
Full text linkWe propose a concrete experiment to probe the non-equilibrium local dynamics
of the one-dimensional Bose-Hubbard model using a trapped ion system consisting
of a linear chain of few Ba^+ ions prepared in a state of transverse motional
mode which corresponds to a fixed number of phonons per ion. These phonons are
well-known to be described by an effective Bose-Hubbard model. We propose a
protocol which leads to a sudden local sign reversal of the on-site interaction
strength of this Hubbard model at one of the sites and demonstrate that the
subsequent non-equilibrium dynamics of the model can be experimentally probed
by measuring the time-dependent phonon number in a specific motional state of
the Ba+ ions. We back our experimental proposal with exact numerical
calculation of the dynamics of a Bose-Hubbard model subsequent to a local
quench.Comment: The submission contains 5 pages and 4 figure
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