16 research outputs found
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
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
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
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
Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
Lattice models forming bands with higher Chern number offer an intriguing
possibility for new phases of matter with no analogue in continuum Landau
levels. Here, we establish the existence of a number of new bulk insulating
states at fractional filling in flat bands with Chern number , forming
in a recently proposed pyrochlore model with strong spin-orbit coupling. In
particular, we find compelling evidence for a series of stable states at
for fermions as well as bosonic states at . By
examining the topological ground state degeneracies and the excitation
structure as well as the entanglement spectrum, we conclude that these states
are Abelian. We also explicitly demonstrate that these states are nevertheless
qualitatively different from conventional quantum Hall (multilayer) states due
to the novel properties of the underlying band structure.Comment: 5+4 pages. Final version. Main text as published, some extra data in
the supplementary materia
Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
Using infinite projected entangled pair states (iPEPS), exact
diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg
model undergoes a spontaneous dimerization on the square lattice, in contrast
to its SU(2) and SU(3) counterparts, which develop Neel and three-sublattice
stripe-like long-range order. Since the ground state of a dimer is not a
singlet for SU(4) but a 6-dimensional irrep, this leaves the door open for
further symmetry breaking. We provide evidence that, unlike in SU(4) ladders,
where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is
additionally broken, leading to a gapless spectrum in spite of the broken
translational symmetry.Comment: 5 pages, 4 figures, minor changes, references adde
Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
We present a detailed analysis of bi-partite entanglement in the non-Abelian
Moore-Read fractional quantum Hall state of bosons and fermions on the torus.
In particular, we show that the entanglement spectra can be decomposed into
intricate combinations of different sectors of the conformal field theory
describing the edge physics, and that the edge level counting and tower
structure can be microscopically understood by considering the vicinity of the
thin-torus limit. We also find that the boundary entropy density of the
Moore-Read state is markedly higher than in the Laughlin states investigated so
far. Despite the torus geometry being somewhat more involved than in the sphere
geometry, our analysis and insights may prove useful when adopting entanglement
probes to other systems that are more easily studied with periodic boundary
conditions, such as fractional Chern insulators and lattice problems in
general.Comment: 13 pages, 8 figures, published version on PR