17,027 research outputs found
Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables
We show that the critical point of the two-dimensional Bose-Hubbard model can
be easily found through studies of either on-site atom number fluctuations or
the nearest-neighbor two-point correlation function (the expectation value of
the tunnelling operator). Our strategy to locate the critical point is based on
the observation that the derivatives of these observables with respect to the
parameter that drives the superfluid-Mott insulator transition are singular at
the critical point in the thermodynamic limit. Performing the quantum Monte
Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this
technique leads to the accurate determination of the position of its critical
point. Our results can be easily extended to the three-dimensional Bose-Hubbard
model and different Hubbard-like models. They provide a simple
experimentally-relevant way of locating critical points in various cold atomic
lattice systems.Comment: 8 pages, rewritten title, abstract & introductio
Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals
We show that the nearest-neighbor spacing distribution for a model that
consists of random points uniformly distributed on a self-similar fractal is
the Brody distribution of random matrix theory. In the usual context of
Hamiltonian systems, the Brody parameter does not have a definite physical
meaning, but in the model considered here, the Brody parameter is actually the
fractal dimension. Exploiting this result, we introduce a new model for a
crossover transition between Poisson and Wigner statistics: random points on a
continuous family of self-similar curves with fractal dimension between 1 and
2. The implications to quantum chaos are discussed, and a connection to
conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image
available (upon request) from the author
HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces
Nearest neighbor searching of large databases in high-dimensional spaces is
inherently difficult due to the curse of dimensionality. A flavor of
approximation is, therefore, necessary to practically solve the problem of
nearest neighbor search. In this paper, we propose a novel yet simple indexing
scheme, HD-Index, to solve the problem of approximate k-nearest neighbor
queries in massive high-dimensional databases. HD-Index consists of a set of
novel hierarchical structures called RDB-trees built on Hilbert keys of
database objects. The leaves of the RDB-trees store distances of database
objects to reference objects, thereby allowing efficient pruning using distance
filters. In addition to triangular inequality, we also use Ptolemaic inequality
to produce better lower bounds. Experiments on massive (up to billion scale)
high-dimensional (up to 1000+) datasets show that HD-Index is effective,
efficient, and scalable.Comment: PVLDB 11(8):906-919, 201
Exchange couplings for Mn ions in CdTe: validity of spin models for dilute magnetic II-VI semiconductors
We employ density-functional theory (DFT) in the generalized gradient
approximation (GGA) and its extensions GGA+ and GGA+Gutzwiller to calculate
the magnetic exchange couplings between pairs of Mn ions substituting Cd in a
CdTe crystal at very small doping. DFT(GGA) overestimates the exchange
couplings by a factor of three because it underestimates the charge-transfer
gap in Mn-doped II-VI semiconductors. Fixing the nearest-neighbor coupling
to its experimental value in GGA+, in GGA+Gutzwiller, or by a simple
scaling of the DFT(GGA) results provides acceptable values for the exchange
couplings at 2nd, 3rd, and 4th neighbor distances in Cd(Mn)Te, Zn(Mn)Te,
Zn(Mn)Se, and Zn(Mn)S. In particular, we recover the experimentally observed
relation . The filling of the Mn 3-shell is not integer which
puts the underlying Heisenberg description into question. However, using a
few-ion toy model the picture of a slightly extended local moment emerges so
that an integer -shell filling is not a prerequisite for equidistant
magnetization plateaus, as seen in experiment.Comment: 12 pages, 10 figure
Gutzwiller study of extended Hubbard models with fixed boson densities
We studied all possible ground states, including supersolid (SS) phases and
phase separations of hard-core- and soft-core-extended Bose--Hubbard models
with fixed boson densities by using the Gutzwiller variational wave function
and the linear programming method. We found that the phase diagram of the
soft-core model depends strongly on its transfer integral. Furthermore, for a
large transfer integral, we showed that an SS phase can be the ground state
even below or at half filling against the phase separation. We also found that
the density difference between nearest-neighbor sites, which indicates the
density order of the SS phase, depends strongly on the boson density and
transfer integral.Comment: 14 pages, 14 figures, to be published in Phys. Rev.
Structure of plastically compacting granular packings
The developing structure in systems of compacting ductile grains were studied
experimentally in two and three dimensions. In both dimensions, the peaks of
the radial distribution function were reduced, broadened, and shifted compared
with those observed in hard disk- and sphere systems. The geometrical
three--grain configurations contributing to the second peak in the radial
distribution function showed few but interesting differences between the
initial and final stages of the two dimensional compaction. The evolution of
the average coordination number as function of packing fraction is compared
with other experimental and numerical results from the literature. We conclude
that compaction history is important for the evolution of the structure of
compacting granular systems.Comment: 12 pages, 12 figure
A tetrahedral space-filling curve for non-conforming adaptive meshes
We introduce a space-filling curve for triangular and tetrahedral
red-refinement that can be computed using bitwise interleaving operations
similar to the well-known Z-order or Morton curve for cubical meshes. To store
sufficient information for random access, we define a low-memory encoding using
10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that
compute the parent, children, and face-neighbors of a mesh element in constant
time, as well as the next and previous element in the space-filling curve and
whether a given element is on the boundary of the root simplex or not. Our
presentation concludes with a scalability demonstration that creates and adapts
selected meshes on a large distributed-memory system.Comment: 33 pages, 12 figures, 8 table
Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions
By removing one empty site between two occupied sites, we map the ground
states of chains of hardcore bosons and spinless fermions with infinite
nearest-neighbor repulsion to ground states of chains of hardcore bosons and
spinless fermions without nearest-neighbor repulsion respectively, and
ultimately in terms of the one-dimensional Fermi sea. We then introduce the
intervening-particle expansion, where we write correlation functions in such
ground states as a systematic sum over conditional expectations, each of which
can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various
ground-state correlation functions are calculated for the bosonic and fermionic
chains with infinite nearest-neighbor repulsion, as well as for a ladder model
of spinless fermions with infinite nearest-neighbor repulsion and correlated
hopping in three limiting cases. We find that the decay of these correlation
functions are governed by surprising power-law exponents.Comment: 20 pages, 18 figures, RevTeX4 clas
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