36,406 research outputs found
Self-dual Chern-Simons solitons in noncommutative space
We construct exact soliton solutions to the Chern-Simons-Higgs system in
noncommutative space, for non-relativistic and relativistic models. In both
cases we find regular vortex-like solutions to the BPS equations which approach
the ordinary selfdual non-topological and topological solitons when the
noncommutative parameter goes to zero.Comment: 15 pages, 4 figure
The k-metric dimension of a graph
As a generalization of the concept of a metric basis, this article introduces
the notion of -metric basis in graphs. Given a connected graph , a
set is said to be a -metric generator for if the elements
of any pair of different vertices of are distinguished by at least
elements of , i.e., for any two different vertices , there exist
at least vertices such that for every . A metric generator of minimum
cardinality is called a -metric basis and its cardinality the -metric
dimension of . A connected graph is -metric dimensional if is the
largest integer such that there exists a -metric basis for . We give a
necessary and sufficient condition for a graph to be -metric dimensional and
we obtain several results on the -metric dimension
Entanglement properties of spin models in triangular lattices
The different quantum phases appearing in strongly correlated systems as well
as their transitions are closely related to the entanglement shared between
their constituents. In 1D systems, it is well established that the entanglement
spectrum is linked to the symmetries that protect the different quantum phases.
This relation extends even further at the phase transitions where a direct link
associates the entanglement spectrum to the conformal field theory describing
the former. For 2D systems much less is known. The lattice geometry becomes a
crucial aspect to consider when studying entanglement and phase transitions.
Here, we analyze the entanglement properties of triangular spin lattice models
by considering also concepts borrowed from quantum information theory such as
geometric entanglement.Comment: 19 pages, 8 figure
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