4,413 research outputs found
Statistical transmutation in doped quantum dimer models
We prove a "statistical transmutation" symmetry of doped quantum dimer models
on the square, triangular and kagome lattices: the energy spectrum is invariant
under a simultaneous change of statistics (i.e. bosonic into fermionic or
vice-versa) of the holes and of the signs of all the dimer resonance loops.
This exact transformation enables to define duality equivalence between doped
quantum dimer Hamiltonians, and provides the analytic framework to analyze
dynamical statistical transmutations. We investigate numerically the doping of
the triangular quantum dimer model, with special focus on the topological Z2
dimer liquid. Doping leads to four (instead of two for the square lattice)
inequivalent families of Hamiltonians. Competition between phase separation,
superfluidity, supersolidity and fermionic phases is investigated in the four
families.Comment: 3 figure
Diagnosing order by disorder in quantum spin systems
In this paper we study the frustrated J1-J2 quantum Heisenberg model on the
square lattice for J2 > 2J1, in a magnetic field. In this regime the classical
system is known to have a degenerate manifold of lowest energy configurations,
where standard thermal order by disorder occurs. In order to study its quantum
version we use a path integral formulation in terms of coherent states. We show
that the classical degeneracy in the plane transverse to the magnetic field is
lifted by quantum fluctuations. Collinear states are then selected, in a
similar pattern to that set by thermal order by disorder, leaving a Z2
degeneracy. A careful analysis reveals a purely quantum mechanical effect given
by the tunneling between the two minima selected by fluctuations. The effective
description contains two planar (XY -like) fields conjugate to the total
magnetization and the difference of the two sublattice magnetizations. Disorder
in either or both of these fields produces the locking of their conjugate
observables. Furthermore, within this scenario we argue that the quantum state
is close to a product state.Comment: 8 pages, 3 figure
Optimizing Mathematical Morphology for Image Segmentation and Vision-based Path Planning in Robotic Environments
Decentralized dynamic task allocation for UAVs with limited communication range
We present the Limited-range Online Routing Problem (LORP), which involves a
team of Unmanned Aerial Vehicles (UAVs) with limited communication range that
must autonomously coordinate to service task requests. We first show a general
approach to cast this dynamic problem as a sequence of decentralized task
allocation problems. Then we present two solutions both based on modeling the
allocation task as a Markov Random Field to subsequently assess decisions by
means of the decentralized Max-Sum algorithm. Our first solution assumes
independence between requests, whereas our second solution also considers the
UAVs' workloads. A thorough empirical evaluation shows that our workload-based
solution consistently outperforms current state-of-the-art methods in a wide
range of scenarios, lowering the average service time up to 16%. In the
best-case scenario there is no gap between our decentralized solution and
centralized techniques. In the worst-case scenario we manage to reduce by 25%
the gap between current decentralized and centralized techniques. Thus, our
solution becomes the method of choice for our problem
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