910 research outputs found
Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg
spins of large spin length is a highly frustrated model with an macroscopic
degeneracy of classical ground states. The zero-point energy of (harmonic
order) spin wave fluctuations distinguishes a subset of these states. I derive
an approximate but illuminating {\it effective Hamiltonian}, acting within the
subspace of Ising spin configurations representing the {\it collinear} ground
states. It consists of products of Ising spins around loops, i.e has the form
of a lattice gauge theory. The remaining ground state entropy is still
infinite but not extensive, being for system size . All these
ground states have unit cells bigger than those considered previously.Comment: 4pp, one figur
Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
We study the phase diagram of a frustrated spin-1/2 ferromagnetic chain with
anisotropic exchange interactions in an external magnetic field, using the
density matrix renormalization group method. We show that an easy-axis
anisotropy enhances the tendency towards multimagnon bound states, while an
easy-plane anisotropy favors chirally ordered phases. In particular, a moderate
easy-plane anisotropy gives rise to a quantum phase transition at intermediate
magnetization. We argue that this transition is related to the finite-field
phase transition experimentally observed in the spin-1/2 compound LiCuVO_4.Comment: The final published versio
Simplex solid states of SU(N) quantum antiferromagnets
I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous
to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT),
in which the singlets are extended over N-site simplices. As with the valence
bond solids, the new simplex solid (SS) states are extinguished by certain
local projection operators, allowing us to construct Hamiltonians with local
interactions which render the SS states exact ground states. Using a coherent
state representation, we show that the quantum correlations in each SS state
are calculable as the finite temperature correlations of an associated
classical model, with N-spin interactions, on the same lattice. In three and
higher dimensions, the SS states can spontaneously break SU(N) and exhibit
N-sublattice long-ranged order, as a function of a discrete parameter which
fixes the local representation of SU(N). I analyze this transition using a
classical mean field approach. For N>2 the ordered state is selected via an
"order by disorder" mechanism. As in the AKLT case, the bulk representations
fractionalize at an edge, and the ground state entropy is proportional to the
volume of the boundary.Comment: 14 pages, 8 figures, minor typos correcte
Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite
In Volborthite, spin-1/2 moments form a distorted Kagom\'e lattice, of corner
sharing isosceles triangles with exchange constants on two bonds and
on the third bond. We study the properties of such spin systems, and show that
despite the distortion, the lattice retains a great deal of frustration.
Although sub-extensive, the classical ground state degeneracy remains very
large, growing exponentially with the system perimeter. We consider degeneracy
lifting by thermal and quantum fluctuations. To linear (spin wave) order, the
degeneracy is found to stay intact. Two complementary approaches are therefore
introduced, appropriate to low and high temperatures, which point to the same
ordered pattern. In the low temperature limit, an effective chirality
Hamiltonian is derived from non-linear spin waves which predicts a transition
on increasing , from type order to a new
ferrimagnetic {\em striped chirality} order with a doubled unit cell. This is
confirmed by a large-N approximation on the O() model on this lattice. While
the saddle point solution produces a line degeneracy, corrections
select the non-trivial wavevector of the striped chirality state. The quantum
limit of spin 1/2 on this lattice is studied via exact small system
diagonalization and compare well with experimental results at intermediate
temperatures. We suggest that the very low temperature spin frozen state seen
in NMR experiments may be related to the disconnected nature of classical
ground states on this lattice, which leads to a prediction for NMR line shapes.Comment: revised, section V about exact diagonalization is extensively
rewritten, 17 pages, 11 figures, RevTex 4, accepted by Phys. Rev.
Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices
in a strong external magnetic field are mapped onto hard-core lattice gases
with an extended exclusion region. The effective models are studied by the
exchange Monte Carlo simulations and by the transfer matrix method. The
transition point and the critical exponents are obtained numerically for a
square-lattice gas of particles with the second-neighbor exclusion, which
describes a checkerboard antiferromagnet. The exact structure of the magnon
crystal state is determined for a pyrochlore antiferromagnet.Comment: 11 pages, accepted versio
Conserved Growth on Vicinal Surfaces
A crystal surface which is miscut with respect to a high symmetry plane
exhibits steps with a characteristic distance. It is argued that the continuum
description of growth on such a surface, when desorption can be neglected, is
given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo,
and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A
one--loop dynamical renormalization group calculation yields the values of the
dynamical exponent and the roughness exponent which are shown to be the same as
in the isotropic case. The results presented here should apply in particular to
growth under conditions which are typical for molecular beam epitaxy.Comment: 10 pages, uses revte
Influence of lattice distortions in classical spin systems
We investigate a simple model of a frustrated classical spin chain coupled to
adiabatic phonons under an external magnetic field. A thorough study of the
magnetization properties is carried out both numerically and analytically. We
show that already a moderate coupling with the lattice can stabilize a plateau
at 1/3 of the saturation and discuss the deformation of the underlying lattice
in this phase. We also study the transition to saturation where either a first
or second order transition can occur, depending on the couplings strength.Comment: Submitted to Phys. Rev.
Spin-orbit effects in NaIrO, a hyper-kagom\'{e} lattice antiferromagnet
We consider spin-orbit coupling effects in NaIrO, a material in
which Ir spins form an hyper-kagom\'{e} lattice, a three-dimensional
network of corner-sharing triangles. We argue that both low temperature
thermodynamic measurements and the impurity susceptibility induced by dilute
substitution of Ti for Ir are suggestive of significant spin-orbit effects.
Because of uncertainties in the crystal-field parameters, we consider two
limits in which the spin-orbit coupling is either weak or strong compared to
the non-cubic atomic splittings. A semi-microscopic calculation of the exchange
Hamiltonian confirms that indeed large antisymmetric Dzyaloshinskii-Moriya (DM)
and/or symmetric exchange anisotropy may be present. In the strong spin-orbit
limit, the Ir-O-Ir superexchange contribution consists of unfrustrated strong
symmetric exchange anisotropy, and we suggest that spin-liquid behavior is
unlikely. In the weak spin-orbit limit, and for strong spin-orbit and direct
Ir-Ir exchange, the Hamiltonian consists of Heisenberg and DM interactions. The
DM coupling is parametrized by a three component DM vector (which must be
determined empirically). For a range of orientation of this vector, frustration
is relieved and an ordered state occurs. For other orientations, even the
classical ground states are very complex. We perform spin-wave and exact
diagonalization calculations which suggest the persistence of a quantum spin
liquid in the latter regime. Applications to NaIrO and broader
implications are discussed.Comment: 22 pages, 15 figures. submit to prb. New references are adde
Bohr-Sommerfeld quantization of spin Hamiltonians
The Bohr-Sommerfeld rule for a spin system is obtained, including the first
quantum corrections. The rule applies to both integer and half-integer spin,
and respects Kramers degeneracy for time-reversal invariant systems. It is
tested for various models, in particular the Lipkin-Meshkov-Glick model, and
found to agree very well with exact results.Comment: Revtex 4, no figures, 1 tabl
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