28 research outputs found
Low energy excitations of the kagome antiferromagnet and the spin gap issue
In this paper we report the latest results of exact diagonalizations of SU(2)
invariant models on various lattices (square, triangular, hexagonal,
checkerboard and kagome lattices). We focus on the low lying levels in each S
sector. The differences in behavior between gapless systems and gapped ones are
exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on
the kagome lattice is discussed. A rough estimate of the spin susceptibility in
such an hypothesis is given.The evolution of the intra-S channel spectra under
the effect of a small perturbation is consistent with the proximity of a
quantum critical point. We emphasize that the very small intra-S channel energy
scale observed in exact spectra is a very interesting information to understand
the low T dynamics of this model.Comment: 6 pages, 5 figures, revised version with a more extended discussion
on the issue of a possible proximity with a quantum critical point, a few
more details and references, a modified Fig
Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions
The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than
one is discussed. It is explained why the variational wave-function built by
the previous authors is of no help to prove the theorem in dimension larger
than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson,
Read and Chakraborty gives a strong support to the assertion that the theorem
is indeed valid in any dimension. Some illustrations of the general ideas are
displayed on exact spectra.Comment: 12 pages, LaTeX with 4 EPS figures embedded in the documen
Spin Liquid in the Multiple-Spin Exchange model on the Triangular lattice: 3He on graphite
Using exact diagonalizations, we investigate the T=0 phase diagram of the
Multi-Spin Exchange (MSE) model on the triangular lattice: we find a transition
separating a ferromagnetic phase from a non-magnetic gapped Spin Liquid phase.
Systems far enough from the ferromagnetic transition have a metamagnetic
behavior with magnetization plateaus at m/m_sat=0 and 1/2. The MSE has been
proposed to describe solid 3He films adsorbed onto graphite, thus we compute
the MSE heat capacity for parameters in the low density range of the 2nd layer
and find a double-peak structure.Comment: Revtex, 4 pages, 4 figures. Accepted to Phys. Rev. Let
A Schwinger-boson approach to the kagome with Dzyaloshinskii-Moriya interactions: phase diagram and dynamical structure factors
We have obtained the zero-temperature phase diagram of the kagome
antiferromagnet with Dzyaloshinskii-Moriya interactions in Schwinger-boson
mean-field theory. We find quantum phase transitions (first or second order)
between different topological spin liquids and Neel ordered phases (either the
state or the so-called Q=0 state). In the regime of
small Schwinger-boson density, the results bear some resemblances with exact
diagonalization results and we briefly discuss some issues of the mean-field
treatment. We calculate the equal-time structure factor (and its angular
average to allow for a direct comparison with experiments on powder samples),
which extends earlier work on the classical kagome to the quantum regime. We
also discuss the dynamical structure factors of the topological spin liquid and
the Neel ordered phase.Comment: 8 pages, 9 figure
The Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters
The nearest neighbor antiferromagnetic Heisenberg model is
considered for spins sitting on the vertices of clusters with the connectivity
of fullerene molecules and a number of sites ranging from 24 to 32. Using
the permutational and spin inversion symmetries of the Hamiltonian the low
energy spectrum is calculated for all the irreducible representations of the
symmetry group of each cluster. Frustration and connectivity result in
non-trivial low energy properties, with the lowest excited states being
singlets except for . Same hexagon and same pentagon correlations are the
most effective in the minimization of the energy, with the
symmetry cluster having an unusually strong singlet intra-pentagon correlation.
The magnetization in a field shows no discontinuities unlike the icosahedral
fullerene clusters, but only plateaux with the most pronounced for
. The spatial symmetry as well as the connectivity of the clusters appear
to be important for the determination of their magnetic properties.Comment: Extended to include low energy spectra, correlation functions and
magnetization data of clusters up to 32 site
Disorder effects in the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
The recent NMR experiments on ZnCu3(OH)6Cl2 motivate our study of the effect
of non- magnetic defects on the antiferromagnetic spin-1/2 kagome lattice. We
use exact diagonalization methods to study the effect of two such defects on
finite size systems. Our results, obtained without adjustable parameters, are
in good quantitative agreement with recent Oxygen 17 NMR data. They provide
support for the experimental interpretation of the presence of defects within
the kagome layers due to Zn/Cu substitutions. Our results also show that
disorder effects become relevant at lower temperatures, raising questions about
the experimental evidence for the absence of an intrinsic spin gap in the
kagome 2D layers.Comment: 5 pages, 4 figure
Lattice symmetries and regular states in classical frustrated antiferromagnets
We consider some classical and frustrated lattice spin models with global
O(3) spin symmetry. There is no general analytical method to find a
ground-state if the spin dependence of the Hamiltonian is more than quadratic
(i.e. beyond the Heisenberg model) and/or if the lattice has more than one site
per unit cell. To deal with these situations, we introduce a family of
variational spin configurations, dubbed "regular states", which respect all the
lattice symmetries modulo global O(3) spin transformations (rotations and/or
spin flips). The construction of these states is explicited through a group
theoretical approach, and all the regular states on the square, triangular,
honeycomb and kagome lattices are listed. Their equal time structure factors
and powder-averages are shown for comparison with experiments. All the well
known N\'eel states with 2 or 3 sublattices appear amongst regular states on
various lattices, but the regular states also encompass exotic non-planar
states with cubic, tetrahedral or cuboctahedral geometry of the T=0 order
parameter. Whatever the details of the Hamiltonian (with the same symmetry
group), a large fraction of these regular states are energetically stationary
with respect to small deviations of the spins. In fact these regular states
appear as exact ground-states in a very large range of parameter space of the
simplest models that we have been looking at. As examples, we display the
variational phase diagrams of the J1-J2-J3 Heisenberg model on all the previous
lattices as well as that of the J1-J2-K ring-exchange model on square and
triangular lattices.Comment: 15 pages, 12 figures, 1 tabl
Magneto-elastic effects and magnetization plateaus in two dimensional systems
We show the importance of both strong frustration and spin-lattice coupling
for the stabilization of magnetization plateaus in translationally invariant
two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model
coupled to adiabatic phonons under an external magnetic field. At zero
magnetization, simple structures with two or at most four spins per unit cell
are stabilized, forming dimers or plaquettes, respectively. A much
richer scenario is found in the case of magnetization , where larger
unit cells are formed with non-trivial spin textures and an analogy with the
corresponding classical Ising model is detectable. Specific predictions on
lattice distortions and local spin values can be directly measured by X-rays
and Nuclear Magnetic Resonance experiments.Comment: 4 pages and 4 figure
Extended Quantum Dimer Model and novel valence-bond phases
We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so
as to construct a concrete example of the model which exhibits the first-order
phase transition between different valence-bond solids suggested recently by
Batista and Trugman and look for the possibility of other exotic dimer states.
We show that our model contains three exotic valence-bond phases (herringbone,
checkerboard and dimer smectic) in the ground-state phase diagram and that it
realizes the phase transition from the staggered valence-bond solid to the
herringbone one. The checkerboard phase has four-fold rotational symmetry,
while the dimer smectic, in the absence of quantum fluctuations, has massive
degeneracy originating from partial ordering only in one of the two spatial
directions. A resonance process involving three dimers resolves this massive
degeneracy and dimer smectic gets ordered (order from disorder).Comment: 20 pages, 13 figures, accepted for publication in J. Stat. Mec
Spontaneous order in the highly frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome lattice due to the Dzyaloshinskii-Moriya anisotropy
The spin-1/2 Ising-Heisenberg model on the triangulated Kagome
(triangles-in-triangles) lattice is exactly solved by establishing a precise
mapping correspondence to the simple spin-1/2 Ising model on Kagome lattice. It
is shown that the disordered spin liquid state, which otherwise occurs in the
ground state of this frustrated spin system on assumption that there is a
sufficiently strong antiferromagnetic intra-trimer interaction, is eliminated
from the ground state by arbitrary but non-zero Dzyaloshinskii-Moriya
anisotropy.Comment: 4 pages, 3 figures, to be presented at conference Highly Frustrated
Magnetism, 7-12 September 2008, Braunschweig, German