22,156 research outputs found
Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
We determine the existence of critical lines in dimerized quantum spin
ladders in their phase diagram of coupling constants using the finite-size DMRG
algorithm. We consider both staggered and columnar dimerization patterns, and
antiferromagnetic and ferromagnetic inter-leg couplings. The existence of
critical phases depends on the precise combination of these patterns. The
nature of the massive phases separating the critical lines are characterized
with generalized string order parameters that determine their valence bond
solid (VBS) content.Comment: 9 pages 10 figure
Competing many-body interactions in systems of trapped ions
We propose and theoretically analyse an experimental configuration in which
lasers induce 3-spin interactions between trapped ions.By properly choosing the
intensities and frequencies of the lasers, 3-spin couplings may be dominant or
comparable to 2-spin terms and magnetic fields. In this way, trapped ions can
be used to study exotic quantum phases which do not have a counterpart in
nature. We study the conditions for the validity of the effective 3-spin
Hamiltonian, and predict qualitatively the quantum phase diagram of the system.Comment: RevTex4 file, color figure
Quantum Google in a Complex Network
We investigate the behavior of the recently proposed quantum Google
algorithm, or quantum PageRank, in large complex networks. Applying the quantum
algorithm to a part of the real World Wide Web, we find that the algorithm is
able to univocally reveal the underlying scale-free topology of the network and
to clearly identify and order the most relevant nodes (hubs) of the graph
according to their importance in the network structure. Moreover, our results
show that the quantum PageRank algorithm generically leads to changes in the
hierarchy of nodes. In addition, as compared to its classical counterpart, the
quantum algorithm is capable to clearly highlight the structure of secondary
hubs of the network, and to partially resolve the degeneracy in importance of
the low lying part of the list of rankings, which represents a typical
shortcoming of the classical PageRank algorithm. Complementary to this study,
our analysis shows that the algorithm is able to clearly distinguish scale-free
networks from other widespread and important classes of complex networks, such
as Erd\H{o}s-R\'enyi networks and hierarchical graphs. We show that the ranking
capabilities of the quantum PageRank algorithm are related to an increased
stability with respect to a variation of the damping parameter that
appears in the Google algorithm, and to a more clearly pronounced power-law
behavior in the distribution of importance among the nodes, as compared to the
classical algorithm. Finally, we study to which extent the increased
sensitivity of the quantum algorithm persists under coordinated attacks of the
most important nodes in scale-free and Erd\H{o}s-R\'enyi random graphs
Universality Classes of Diagonal Quantum Spin Ladders
We find the classification of diagonal spin ladders depending on a
characteristic integer in terms of ferrimagnetic, gapped and critical
phases. We use the finite algorithm DMRG, non-linear sigma model and
bosonization techniques to prove our results. We find stoichiometric contents
in cuprate planes that allow for the existence of weakly interacting
diagonal ladders.Comment: REVTEX4 file, 3 color figures, 1 tabl
Topology induced anomalous defect production by crossing a quantum critical point
We study the influence of topology on the quench dynamics of a system driven
across a quantum critical point. We show how the appearance of certain edge
states, which fully characterise the topology of the system, dramatically
modifies the process of defect production during the crossing of the critical
point. Interestingly enough, the density of defects is no longer described by
the Kibble-Zurek scaling, but determined instead by the non-universal
topological features of the system. Edge states are shown to be robust against
defect production, which highlights their topological nature.Comment: Phys. Rev. Lett. (to be published
On the generalized Feng-Rao numbers of numerical semigroups generated by intervals
We give some general results concerning the computation of the generalized
Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup
generated by an interval, a formula for the Feng-Rao number is
obtained.Comment: 23 pages, 6 figure
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