370 research outputs found
Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
We examine the phase diagram of the half-filled one-dimensional extended
Hubbard model using quantum information entropies within the density-matrix
renormalization group. It is well known that there is a charge-density-wave
phase at large nearest-neighbor and small on-site Coloumb repulsion and a
spin-density-wave at small nearest-neighbor and large on-site Coloumb
repulsion. At intermediate Coulomb interaction strength, we find an additional
narrow region of a bond-order phase between these two phases. The phase
transition line for the transition out of the charge-density-wave phase changes
from first-order at strong coupling to second-order in a parameter regime where
all three phases are present. We present evidence that the additional
phase-transition line between the spin-density-wave and bond-order phases is
infinite order. While these results are in agreement with recent numerical
work, our study provides an independent, unbiased means of determining the
phase boundaries by using quantum information analysis, yields values for the
location of some of the phase boundaries that differ from those previously
found, and provides insight into the limitations of numerical methods in
determining phase boundaries, especially those of infinite-order transitions.Comment: 8 pages, 7 figure
Grafting and Poisson structure in (2+1)-gravity with vanishing cosmological constant
We relate the geometrical construction of (2+1)-spacetimes via grafting to
phase space and Poisson structure in the Chern-Simons formulation of
(2+1)-dimensional gravity with vanishing cosmological constant on manifolds of
topology , where is an orientable two-surface of genus
. We show how grafting along simple closed geodesics \lambda is
implemented in the Chern-Simons formalism and derive explicit expressions for
its action on the holonomies of general closed curves on S_g. We prove that
this action is generated via the Poisson bracket by a gauge invariant
observable associated to the holonomy of . We deduce a symmetry
relation between the Poisson brackets of observables associated to the Lorentz
and translational components of the holonomies of general closed curves on S_g
and discuss its physical interpretation. Finally, we relate the action of
grafting on the phase space to the action of Dehn twists and show that grafting
can be viewed as a Dehn twist with a formal parameter satisfying
.Comment: 43 pages, 10 .eps figures; minor modifications: 2 figures added,
explanations added, typos correcte
Entanglement Entropy of Random Fractional Quantum Hall Systems
The entanglement entropy of the and quantum Hall
states in the presence of short range random disorder has been calculated by
direct diagonalization. A microscopic model of electron-electron interaction is
used, electrons are confined to a single Landau level and interact with long
range Coulomb interaction. For very weak disorder, the values of the
topological entanglement entropy are roughly consistent with expected
theoretical results. By considering a broader range of disorder strengths, the
fluctuation in the entanglement entropy was studied in an effort to detect
quantum phase transitions. In particular, there is a clear signature of a
transition as a function of the disorder strength for the state.
Prospects for using the density matrix renormalization group to compute the
entanglement entropy for larger system sizes are discussed.Comment: 29 pages, 16 figures; fixed figures and figure captions; revised
fluctuation calculation
On the extension of stringlike localised sectors in 2+1 dimensions
In the framework of algebraic quantum field theory, we study the category
\Delta_BF^A of stringlike localised representations of a net of observables O
\mapsto A(O) in three dimensions. It is shown that compactly localised (DHR)
representations give rise to a non-trivial centre of \Delta_BF^A with respect
to the braiding. This implies that \Delta_BF^A cannot be modular when
non-trival DHR sectors exist. Modular tensor categories, however, are important
for topological quantum computing. For this reason, we discuss a method to
remove this obstruction to modularity.
Indeed, the obstruction can be removed by passing from the observable net
A(O) to the Doplicher-Roberts field net F(O). It is then shown that sectors of
A can be extended to sectors of the field net that commute with the action of
the corresponding symmetry group. Moreover, all such sectors are extensions of
sectors of A. Finally, the category \Delta_BF^F of sectors of F is studied by
investigating the relation with the categorical crossed product of \Delta_BF^A
by the subcategory of DHR representations. Under appropriate conditions, this
completely determines the category \Delta_BF^F.Comment: 36 pages, 1 eps figure; v2: appendix added, minor corrections and
clarification
A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
We define and discuss classical and quantum gravity in 2+1 dimensions in the
Galilean limit. Although there are no Newtonian forces between massive objects
in (2+1)-dimensional gravity, the Galilean limit is not trivial. Depending on
the topology of spacetime there are typically finitely many topological degrees
of freedom as well as topological interactions of Aharonov-Bohm type between
massive objects. In order to capture these topological aspects we consider a
two-fold central extension of the Galilei group whose Lie algebra possesses an
invariant and non-degenerate inner product. Using this inner product we define
Galilean gravity as a Chern-Simons theory of the doubly-extended Galilei group.
The particular extension of the Galilei group we consider is the classical
double of a much studied group, the extended homogeneous Galilei group, which
is also often called Nappi-Witten group. We exhibit the Poisson-Lie structure
of the doubly extended Galilei group, and quantise the Chern-Simons theory
using a Hamiltonian approach. Many aspects of the quantum theory are determined
by the quantum double of the extended homogenous Galilei group, or Galilei
double for short. We study the representation theory of the Galilei double,
explain how associated braid group representations account for the topological
interactions in the theory, and briefly comment on an associated
non-commutative Galilean spacetime.Comment: 38 pages, 1 figure, references update
Mixing of mineral dust with urban pollution aerosol over Dakar (Senegal): Impact on dust physico-chemical and radiative properties.
In the framework of the Saharan Mineral Dust Experiment (SAMUM) in 2008, the mixing of the urban pollution
plume of Dakar (Senegal) with mineral dust was studied in detail using the German research aircraft Falcon which was
equipped with a nadir-looking high spectral resolution lidar (HSRL) and extensive aerosol in situ instrumentation. The
mineral dust layer as well as the urban pollution plume were probed remotely by the HSRL and in situ. Back trajectory
analyses were used to attribute aerosol samples to source regions.We found that the emission from the region of Dakar
increased the aerosol optical depth (532 nm) from approximately 0.30 over sea and over land east of Dakar to 0.35 in the city outflow. In the urban area, local black carbon (BC) emissions, or soot respectively, contributed more than 75% to aerosol absorption at 530 nm. In the dust layer, the single-scattering albedo at 530 nm was 0.96 � 0.99, whereas
we found a value of 0.908 �± 0.018 for the aerosol dominated by urban pollution. After 6h of transport over the North
Atlantic, the externally mixed mode of secondary aerosol particles had almost completely vanished, whereas the BC
agglomerates (soot) were still externally mixed with mineral dust particles
Generalized Particle Statistics in Two-Dimensions: Examples from the Theory of Free Massive Dirac Field
In the framework of algebraic quantum field theory we analyze the anomalous
statistics exhibited by a class of automorphisms of the observable algebra of
the two-dimensional free massive Dirac field, constructed by fermionic gauge
group methods. The violation of Haag duality, the topological peculiarity of a
two-dimensional space-time and the fact that unitary implementers do not lie in
the global field algebra account for strange behaviour of statistics, which is
no longer an intrinsic property of sectors. Since automorphisms are not inner,
we exploit asymptotic abelianness of intertwiners in order to construct a
braiding for a suitable -tensor subcategory of End(). We
define two inequivalent classes of path connected bi-asymptopias, selecting
only those sets of nets which yield a true generalized statistics operator.Comment: 24 page
Characterization of a ballistic supermirror neutron guide
We describe the beam characteristics of the first ballistic supermirror
neutron guide H113 that feeds the neutron user facility for particle physics
PF1B of the Institute Laue-Langevin, Grenoble (ILL). At present, the neutron
capture flux density of H113 at its 20x6cm2 exit window is 1.35x10^10/cm^2/s,
and will soon be raised to above 2x10^10/cm^2/s. Beam divergence is no larger
than beam divergence from a conventional Ni coated guide. A model is developed
that permits rapid calculation of beam profiles and absolute event rates from
such a beam. We propose a procedure that permits inter-comparability of the
main features of beams emitted from ballistic or conventional neutron guides.Comment: 15 pages, 11 figures, to be submitted to Nuclear Instruments and
Methods
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