16,383 research outputs found
Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillings
We 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
Efficient Learning for Undirected Topic Models
Replicated Softmax model, a well-known undirected topic model, is powerful in
extracting semantic representations of documents. Traditional learning
strategies such as Contrastive Divergence are very inefficient. This paper
provides a novel estimator to speed up the learning based on Noise Contrastive
Estimate, extended for documents of variant lengths and weighted inputs.
Experiments on two benchmarks show that the new estimator achieves great
learning efficiency and high accuracy on document retrieval and classification.Comment: Accepted by ACL-IJCNLP 2015 short paper. 6 page
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