505 research outputs found
Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet
The coupled cluster method is applied to a spin-half model at zero
temperature (), which interpolates between Heisenberg antiferromagnets
(HAF's) on a kagome and a square lattice. With respect to an underlying
triangular lattice the strengths of the Heisenberg bonds joining the
nearest-neighbor (NN) kagome sites are along two of the
equivalent directions and along the third. Sites connected by
bonds are themselves connected to the missing NN non-kagome sites of
the triangular lattice by bonds of strength . When
and the model reduces to the square-lattice HAF. The
magnetic ordering of the system is investigated and its phase diagram
discussed. Results for the kagome HAF limit are among the best available.Comment: 21 pages, 8 figure
Multilevel models of age-related changes in facial shape in adolescents
Here we study the effects of age on facial shape in adolescents by using a method called multilevel principal components analysis (mPCA). An associated multilevel multivariate probability distribution is derived and expressions for the (conditional) probability of age-group membership are presented. This formalism is explored via Monte Carlo (MC) simulated data in the first dataset; where age is taken to increase the overall scale of a three-dimensional facial shape represented by 21 landmark points and all other “subjective” variations are related to the width of the face. Eigenvalue plots make sense and modes of variation correctly identify these two main factors at appropriate levels of the mPCA model. Component scores for both single-level PCA and mPCA show a strong trend with age. Conditional probabilities are shown to predict membership by age group and the Pearson correlation coefficient between actual and predicted group membership is r = 0.99. The effects of outliers added to the MC training data are reduced by the use of robust covariance matrix estimation and robust averaging of matrices. These methods are applied to another dataset containing 12 GPA-scaled (3D) landmark points for 195 shapes from 27 white, male schoolchildren aged 11 to 16 years old. 21% of variation in the shapes for this dataset was accounted for by age. Mode 1 at level 1 (age) via mPCA appears to capture an increase in face height with age, which is consistent with reported pubertal changes in children. Component scores for both single-level PCA and mPCA again show a distinct trend with age. Conditional probabilities are again shown to reflect membership by age group and the Pearson correlation coefficient is given by r = 0.63 in this case. These analyses are an excellent first test of the ability of multilevel statistical methods to model age-related changes in facial shape in adolescents
The frustrated Heisenberg antiferromagnet on the honeycomb lattice: -- model
We study the ground-state (gs) phase diagram of the frustrated spin-1/2
-- antiferromagnet with () on the
honeycomb lattice, using the coupled-cluster method. We present results for the
ground-state energy, magnetic order parameter and plaquette valence-bond
crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for
, where and . The transition at
to the N\'{e}el phase seems to be a continuous deconfined
transition (although we cannot exclude a very narrow intermediate phase in the
range ), while that at is of
first-order type to another quasiclassical antiferromagnetic phase that occurs
in the classical version of the model only at the isolated and highly
degenerate critical point . The spiral phases that are present
classically for all values are absent for all .Comment: 6 pages, 5 figure
The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
We study the ground-state (gs) phase diagram of the frustrated spin-1/2
-- antiferromagnet with on the
honeycomb lattice, using coupled-cluster theory and exact diagonalization
methods. We present results for the gs energy, magnetic order parameter,
spin-spin correlation function, and plaquette valence-bond crystal (PVBC)
susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for , a collinear striped AFM phase for , and a paramagnetic PVBC phase for . The transition at
appears to be of first-order type, while that at is
continuous. Since the N\'eel and PVBC phases break different symmetries our
results favor the deconfinement scenario for the transition at
The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
Starting with the sqrt{3} x sqrt{3} and the q=0 states as reference states we
use the coupled cluster method to high orders of approximation to investigate
the ground state of the Heisenberg antiferromagnet on the kagome lattice for
spin quantum numbers s=1/2,1,3/2,2,5/2, and 3. Our data for the ground-state
energy for s=1/2 are in good agreement with recent large-scale density-matrix
renormalization group and exact diagonalization data. We find that the
ground-state selection depends on the spin quantum number s. While for the
extreme quantum case, s=1/2, the q=0 state is energetically favored by quantum
fluctuations, for any s>1/2 the sqrt{3} x sqrt{3} state is selected. For both
the sqrt{3} x sqrt{3} and the q=0 states the magnetic order is strongly
suppressed by quantum fluctuations. Within our coupled cluster method we get
vanishing values for the order parameter (sublattice magnetization) M for s=1/2
and s=1, but (small) nonzero values for M for s>1. Using the data for the
ground-state energy and the order parameter for s=3/2,2,5/2, and 3 we also
estimate the leading quantum corrections to the classical values.Comment: 7 pages, 6 figure
An Ancient Wolf, Canus lupus, Den and Associated Human Activity in the Southwestern Yukon Territory
The recovery of an ancient hunting artifact in an active Wolf den indicates that Wolf denning sites may be reused for many centuries. It also suggests that traditional practices of predator management by humans may have great antiquity
Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
We use the coupled cluster method to study the zero-temperature properties of
an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2
moments on an infinite spatially anisotropic kagome lattice of corner-sharing
isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange
constants along two of the three lattice directions and along the third. In the classical limit the ground-state (GS)
phase for has collinear ferrimagnetic (N\'{e}el) order where
the -coupled chain spins are ferromagnetically ordered in one direction
with the remaining spins aligned in the opposite direction, while for there exists an infinite GS family of canted ferrimagnetic spin states,
which are energetically degenerate. For the spin-1/2 case we find that quantum
analogs of both these classical states continue to exist as stable GS phases in
some regions of the anisotropy parameter , namely for
for the N\'{e}el state and for (at least part of)
the region for the canted phase. However, they are now
separated by a paramagnetic phase without either sort of magnetic order in the
region , which includes the isotropic
kagome point where the stable GS phase is now believed to be a
topological () spin liquid. Our best numerical estimates are
and
A Recursive Method of the Stochastic State Selection for Quantum Spin Systems
In this paper we propose the recursive stochastic state selection method, an
extension of the recently developed stochastic state selection method in Monte
Carlo calculations for quantum spin systems. In this recursive method we use
intermediate states to define probability functions for stochastic state
selections. Then we can diminish variances of samplings when we calculate
expectation values of the powers of the Hamiltonian. In order to show the
improvement we perform numerical calculations of the spin-1/2
anti-ferromagnetic Heisenberg model on the triangular lattice. Examining
results on the ground state of the 21-site system we confide this method in its
effectiveness. We also calculate the lowest and the excited energy eigenvalues
as well as the static structure factor for the 36-site system. The maximum
number of basis states kept in a computer memory for this system is about 3.6 x
10**7. Employing a translationally invariant initial trial state, we evaluate
the lowest energy eigenvalue within 0.5 % of the statistical errors.Comment: 14 pages, 1 figur
Excited states of quantum many-body interacting systems: A variational coupled-cluster description
We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin . In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.Comment: 17 pages, 4 figure
- …