4,312 research outputs found
Large quantum fluctuations in the strongly coupled spin-1/2 chains of green dioptase: a hidden message from birds and trees
The green mineral dioptase Cu6Si6O18(H2O)6 has been known since centuries and
plays an important role in esoteric doctrines. In particular, the green
dioptase is supposed to grant the skill to speak with trees and to understand
the language of birds. Armed with natural samples of dioptase, we were able to
unravel the magnetic nature of the mineral (presumably with hidden support from
birds and trees) and show that strong quantum fluctuations can be realized in
an essentially framework-type spin lattice of coupled chains, thus neither
frustration nor low-dimensionality are prerequisites. We present a microscopic
magnetic model for the green dioptase. Based on full-potential DFT
calculations, we find two relevant couplings in this system: an
antiferromagnetic coupling J_c, forming spiral chains along the hexagonal c
axis, and an inter-chain ferromagnetic coupling J_d within structural Cu2O6
dimers. To refine the J_c and J_d values and to confirm the proposed spin
model, we perform quantum Monte-Carlo simulations for the dioptase spin
lattice. The derived magnetic susceptibility, the magnetic ground state, and
the sublattice magnetization are in remarkably good agreement with the
experimental data. The refined model parameters are J_c = 78 K and J_d = -37 K
with J_d/J_c ~ -0.5. Despite the apparent three-dimensional features of the
spin lattice and the lack of frustration, strong quantum fluctuations in the
system are evidenced by a broad maximum in the magnetic susceptibility, a
reduced value of the Neel temperature T_N ~ 15 K >> J_c, and a low value of the
sublattice magnetization m = 0.55 Bohr magneton. All these features should be
ascribed to the low coordination number of 3 that outbalances the
three-dimensional nature of the spin lattice.Comment: Dedicated to Stefan-Ludwig Drechsler on the occasion of his 60th
birthday (9 pages, 6 figures
Seeded Graph Matching via Large Neighborhood Statistics
We study a well known noisy model of the graph isomorphism problem. In this
model, the goal is to perfectly recover the vertex correspondence between two
edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of
correctly matched vertex pairs revealed as side information. For seeded
problems, our result provides a significant improvement over previously known
results. We show that it is possible to achieve the information-theoretic limit
of graph sparsity in time polynomial in the number of vertices . Moreover,
we show the number of seeds needed for exact recovery in polynomial-time can be
as low as in the sparse graph regime (with the average degree
smaller than ) and in the dense graph regime.
Our results also shed light on the unseeded problem. In particular, we give
sub-exponential time algorithms for sparse models and an
algorithm for dense models for some parameters, including some that are not
covered by recent results of Barak et al
Monotone graph limits and quasimonotone graphs
The recent theory of graph limits gives a powerful framework for
understanding the properties of suitable (convergent) sequences of
graphs in terms of a limiting object which may be represented by a symmetric
function on , i.e., a kernel or graphon. In this context it is
natural to wish to relate specific properties of the sequence to specific
properties of the kernel. Here we show that the kernel is monotone (i.e.,
increasing in both variables) if and only if the sequence satisfies a
`quasi-monotonicity' property defined by a certain functional tending to zero.
As a tool we prove an inequality relating the cut and norms of kernels of
the form with and monotone that may be of interest in its
own right; no such inequality holds for general kernels.Comment: 38 page
Square-lattice magnetism of diaboleite Pb2Cu(OH)4Cl2
We report on the quasi-two-dimensional magnetism of the natural mineral
diaboleite Pb2Cu(OH)4Cl2 with a tetragonal crystal structure, which is closely
related to that of the frustrated spin-1/2 magnet PbVO3. Magnetic
susceptibility of diaboleite is well described by a Heisenberg spin model on a
diluted square lattice with the nearest-neighbor exchange of J~35 K and about
5% of non-magnetic impurities. The dilution of the spin lattice reflects the
formation of Cu vacancies that are tolerated by the crystal structure of
diaboleite. The weak coupling between the magnetic planes triggers the
long-range antiferromagnetic order below TN~11 K. No evidence of magnetic
frustration is found. We also analyze the signatures of the long-range order in
heat-capacity data, and discuss the capability of identifying magnetic
transitions with heat-capacity measurements.Comment: 10 pages, 10 figures + Supplementary Informatio
The spin gap in malachite Cu2(OH)2CO3 and its evolution under pressure
We report on the microscopic magnetic modeling of the spin-1/2 copper mineral
malachite at ambient and elevated pressures. Despite the layered crystal
structure of this mineral, the ambient-pressure susceptibility and
magnetization data can be well described by an unfrustrated
quasi-one-dimensional magnetic model. Weakly interacting antiferromagnetic
alternating spin chains are responsible for a large spin gap of 120K. Although
the intradimer Cu-O-Cu bridging angles are considerably smaller than the
interdimer angles, density functional theory (DFT) calculations revealed that
the largest exchange coupling of 190K operates within the structural dimers.
The lack of the inversion symmetry in the exchange pathways gives rise to
sizable Dzyaloshinskii-Moriya interactions which were estimated by
full-relativistic DFT+U calculations. Based on available high-pressure crystal
structures, we investigate the exchange couplings under pressure and make
predictions for the evolution of the spin gap. The calculations evidence that
intradimer couplings are strongly pressure-dependent and their evolution
underlies the decrease of the spin gap under pressure. Finally, we assess the
accuracy of hydrogen positions determined by structural relaxation within DFT
and put forward this computational method as a viable alternative to elaborate
experiments
Terrestrial planets across space and time
The study of cosmology, galaxy formation and exoplanets has now advanced to a
stage where a cosmic inventory of terrestrial planets may be attempted. By
coupling semi-analytic models of galaxy formation to a recipe that relates the
occurrence of planets to the mass and metallicity of their host stars, we trace
the population of terrestrial planets around both solar-mass (FGK type) and
lower-mass (M dwarf) stars throughout all of cosmic history. We find that the
mean age of terrestrial planets in the local Universe is Gyr for FGK
hosts and Gyr for M dwarfs. We estimate that hot Jupiters have
depleted the population of terrestrial planets around FGK stars by no more than
, and that only of the terrestrial planets at the
current epoch are orbiting stars in a metallicity range for which such planets
have yet to be confirmed. The typical terrestrial planet in the local Universe
is located in a spheroid-dominated galaxy with a total stellar mass comparable
to that of the Milky Way. When looking at the inventory of planets throughout
the whole observable Universe, we argue for a total of and terrestrial planets around FGK and M
stars, respectively. Due to light travel time effects, the terrestrial planets
on our past light cone exhibit a mean age of just Gyr. These
results are discussed in the context of cosmic habitability, the Copernican
principle and searches for extraterrestrial intelligence at cosmological
distances.Comment: 11 pages, 8 figures. v.2: Accepted for publication in ApJ. Some
changes in quantitative results compared to v.1, mainly due to differences in
IMF assumption
An Interesting Class of Operators with unusual Schatten-von Neumann behavior
We consider the class of integral operators Q_\f on of the form
(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy. We discuss necessary and
sufficient conditions on to insure that is bounded, compact,
or in the Schatten-von Neumann class \bS_p, . We also give
necessary and sufficient conditions for to be a finite rank
operator. However, there is a kind of cut-off at , and for membership in
\bS_{p}, , the situation is more complicated. Although we give
various necessary conditions and sufficient conditions relating to
Q_{\phi}\in\bS_{p} in that range, we do not have necessary and sufficient
conditions. In the most important case , we have a necessary condition and
a sufficient condition, using and modulus of continuity,
respectively, with a rather small gap in between. A second cut-off occurs at
: if \f is sufficiently smooth and decays reasonably fast, then \qf
belongs to the weak Schatten-von Neumann class \wS{1/2}, but never to
\bS_{1/2} unless \f=0.
We also obtain results for related families of operators acting on
and .
We further study operations acting on bounded linear operators on
related to the class of operators Q_\f. In particular we
study Schur multipliers given by functions of the form and
we study properties of the averaging projection (Hilbert-Schmidt projection)
onto the operators of the form Q_\f.Comment: 87 page
Decorated Shastry-Sutherland lattice in the spin-1/2 magnet CdCu2(BO3)2
We report the microscopic magnetic model for the spin-1/2 Heisenberg system
CdCu2(BO3)2, one of the few quantum magnets showing the 1/2-magnetization
plateau. Recent neutron diffraction experiments on this compound [M. Hase et
al., Phys. Rev. B 80, 104405 (2009)] evidenced long-range magnetic order,
inconsistent with the previously suggested phenomenological magnetic model of
isolated dimers and spin chains. Based on extensive density-functional theory
band structure calculations, exact diagonalizations, quantum Monte Carlo
simulations, third-order perturbation theory, as well as high-field
magnetization measurements, we find that the magnetic properties of CdCu2(BO3)2
are accounted for by a frustrated quasi-2D magnetic model featuring four
inequivalent exchange couplings: the leading antiferromagnetic coupling J_d
within the structural Cu2O6 dimers, two interdimer couplings J_t1 and J_t2,
forming magnetic tetramers, and a ferromagnetic coupling J_it between the
tetramers. Based on comparison to the experimental data, we evaluate the ratios
of the leading couplings J_d : J_t1 : J_t2 : J_it = 1 : 0.20 : 0.45 : -0.30,
with J_d of about 178 K. The inequivalence of J_t1 and J_t2 largely lifts the
frustration and triggers long-range antiferromagnetic ordering. The proposed
model accounts correctly for the different magnetic moments localized on
structurally inequivalent Cu atoms in the ground-state magnetic configuration.
We extensively analyze the magnetic properties of this model, including a
detailed description of the magnetically ordered ground state and its evolution
in magnetic field with particular emphasis on the 1/2-magnetization plateau.
Our results establish remarkable analogies to the Shastry-Sutherland model of
SrCu2(BO3)2, and characterize the closely related CdCu2(BO3)2 as a material
realization for the spin-1/2 decorated anisotropic Shastry-Sutherland lattice.Comment: 16 pages, 13 figures, 2 tables. Published version with additional QMC
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