113 research outputs found
Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
We study the directional-ordering transition in the two-dimensional classical
and quantum compass models on the square lattice by means of Monte Carlo
simulations. An improved algorithm is presented which builds on the Wolff
cluster algorithm in one-dimensional subspaces of the configuration space. This
improvement allows us to study classical systems up to . Based on the
new algorithm we give evidence for the presence of strongly anomalous scaling
for periodic boundary conditions which is much worse than anticipated before.
We propose and study alternative boundary conditions for the compass model
which do not make use of extended configuration spaces and show that they
completely remove the problem with finite-size scaling. In the last part, we
apply these boundary conditions to the quantum problem and present a
considerably improved estimate for the critical temperature which should be of
interest for future studies on the compass model. Our investigation identifies
a strong one-dimensional magnetic ordering tendency with a large correlation
length as the cause of the unusual scaling and moreover allows for a precise
quantification of the anomalous length scale involved.Comment: 10 pages, 8 figures; version as publishe
Highly Frustrated Magnetic Clusters: The kagome on a sphere
We present a detailed study of the low-energy excitations of two existing
finite-size realizations of the planar kagome Heisenberg antiferromagnet on the
sphere, the cuboctahedron and the icosidodecahedron. After highlighting a
number of special spectral features (such as the presence of low-lying singlets
below the first triplet and the existence of localized magnons) we focus on two
major issues. The first concerns the nature of the excitations above the
plateau phase at 1/3 of the saturation magnetization Ms. Our exact
diagonalizations for the s=1/2 icosidodecahedron reveal that the low-lying
plateau states are adiabatically connected to the degenerate collinear
``up-up-down'' ground states of the Ising point, at the same time being well
isolated from higher excitations. A complementary physical picture emerges from
the derivation of an effective quantum dimer model which reveals the central
role of the topology and the intrinsic spin s. We also give a prediction for
the low energy excitations and thermodynamic properties of the spin s=5/2
icosidodecahedron Mo72Fe30. In the second part we focus on the low-energy
spectra of the s>1/2 Heisenberg model in view of interpreting the broad
inelastic neutron scattering response reported for Mo72Fe30. To this end we
demonstrate the simultaneous presence of several broadened low-energy ``towers
of states'' or ``rotational bands'' which arise from the large discrete spatial
degeneracy of the classical ground states, a generic feature of highly
frustrated clusters. This semiclassical interpretation is further corroborated
by their striking symmetry pattern which is shown, by an independent group
theoretical analysis, to be a characteristic fingerprint of the classical
coplanar ground states.Comment: 22 pages Added references Corrected typo
Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points
We determine the dynamical dimer correlation functions of quantum dimer
models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices
and the non-bipartite triangular lattice. Based on an algorithmic idea by
Henley, we simulate a stochastic process of classical dimer configurations in
continuous time and perform a stochastic analytical continuation to obtain the
dynamical correlations in momentum space and the frequency domain. This
approach allows us to observe directly the dispersion relations and the
evolution of the spectral intensity within the Brillouin zone beyond the
single-mode approximation. On the square lattice, we confirm analytical
predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0)
and further reveal the existence of shadow bands close to the wavevector (0,0).
On the cubic lattice the spectrum is also gapless but here only a single soft
mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The
soft mode has a quadratic dispersion at very long wavelength, but crosses over
to a linear behavior very rapidly. We believe this to be the remnant of the
linearly dispersing "photon" of the Coulomb phase. Finally the triangular
lattice is in a fully gapped liquid phase where the bottom of the dimer
spectrum exhibits a rich structure. At the M point the gap is minimal and the
spectral response is dominated by a sharp quasiparticle peak. On the other
hand, at the X point the spectral function is much broader. We sketch a
possible explanation based on the crossing of the coherent dimer excitations
into the two-vison continuum.Comment: 16 pages, 7 figures, published versio
Entanglement spectrum of the two dimensional Bose-Hubbard model
We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two
dimensional square lattice at unit filling, both in the Mott insulating and in
the superfluid phase. In the Mott phase, we demonstrate that the ES is
dominated by the physics at the boundary between the two subsystems. On top of
the boundary-local (perturbative) structure, the ES exhibits substructures
arising from one-dimensional dispersions along the boundary. In the superfluid
phase, the structure of the ES is qualitatively different, and reflects the
spontaneously broken U(1) symmetry of the phase. We attribute the basic
low-lying structure to a so-called "tower of states" (TOS) Hamiltonian of the
model. We then discuss how these characteristic structures evolve across the
superfluid to Mott insulator transition and their influence on the behavior of
the entanglement entropies. Finally, we briefly outline the implications of the
ES structure on the efficiency of matrix-product-state based algorithms in two
dimensions.Comment: 4 pages, 4 figures; supplementary materials (4 pages, 2 figures).
Minor changes, few typos corrected. Published versio
Spatial noise correlations of a chain of ultracold fermions - A numerical study
We present a numerical study of noise correlations, i.e., density-density
correlations in momentum space, in the extended fermionic Hubbard model in one
dimension. In experiments with ultracold atoms, these noise correlations can be
extracted from time-of-flight images of the expanding cloud. Using the
density-matrix renormalization group method to investigate the Hubbard model at
various fillings and interactions, we confirm that the shot noise contains full
information on the correlations present in the system. We point out the
importance of the sum rules fulfilled by the noise correlations and show that
they yield nonsingular structures beyond the predictions of bosonization
approaches. Noise correlations can thus serve as a universal probe of order and
can be used to characterize the many-body states of cold atoms in optical
lattices.Comment: 12 pages, 7 figure
Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
We study the entanglement spectrum (ES) of a finite XXZ spin 1/2 chain in the
limit \Delta -> -1^+ for both open and periodic boundary conditions. At
\Delta=-1 (ferromagnetic point) the model is equivalent to the Heisenberg
ferromagnet and its degenerate ground state manifold is the SU(2) multiplet
with maximal total spin. Any state in this so-called "symmetric sector" is an
equal weight superposition of all possible spin configurations. In the gapless
phase at \Delta>-1 this property is progressively lost as one moves away from
the \Delta=-1 point. We investigate how the ES obtained from the states in this
manifold reflects this change, using exact diagonalization and Bethe ansatz
calculations. We find that in the limit \Delta ->-1^+ most of the ES levels
show divergent behavior. Moreover, while at \Delta=-1 the ES contains no
information about the boundaries, for \Delta>-1 it depends dramatically on the
choice of boundary conditions. For both open and periodic boundary conditions
the ES exhibits an elegant multiplicity structure for which we conjecture a
combinatorial formula. We also study the entanglement eigenfunctions, i.e. the
eigenfunctions of the reduced density matrix. We find that the eigenfunctions
corresponding to the non diverging levels mimic the behavior of the state
wavefunction, whereas the others show intriguing polynomial structures. Finally
we analyze the distribution of the ES levels as the system is detuned away from
\Delta=-1.Comment: 21 pages, 8 figures. Minor corrections, references added. Published
versio
Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8
We study the antiferromagnetic spin-1/2 Heisenberg model on the highly
frustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using a
series expansion method. We propose a valence bond crystal with a 72 site unit
cell as a ground state that supports many, very low lying, singlet excitations.
Low energy spinons and triplons are confined to emergent lower-dimensional
motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite
temperature signatures, including an Ising transition, in the magnetic specific
heat due to a multistep breaking of discrete symmetries.Comment: 4 pages, 3 figure
The Polarity of the Gospels in the Exegesis of Origen
In spite of all the hermeneutic research, the allegorizing of the Alexandrians, and above all the exegetical work of Origen, remains a strange phenomenon of the early church. Historians have often smiled indulgently, if they have not scoffed, at those childhood steps of biblical interpretation within ancient Christian theology, from Thomasius more than a century ago up to our present. The possibility of a complete understanding is hindered by the lack of many of Origen's texts in the original language. Many of his commentaries are lost. And yet there are certain indications from which we can learn that Origen did have his sound reasons for his exegetical undertaking. For this, one has to examine the tenth chapter of his Commentary on Joh
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