1,047 research outputs found
An Exactly Solvable Model of Generalized Spin Ladder
A detailed study of an spin ladder model is given. The ladder
consists of plaquettes formed by nearest neighbor rungs with all possible
SU(2)-invariant interactions. For properly chosen coupling constants, the model
is shown to be integrable in the sense that the quantum Yang-Baxter equation
holds and one has an infinite number of conserved quantities. The R-matrix and
L-operator associated with the model Hamiltonian are given in a limiting case.
It is shown that after a simple transformation, the model can be solved via a
Bethe ansatz. The phase diagram of the ground state is exactly derived using
the Bethe ansatz equation
On the dynamics of coupled S=1/2 antiferromagnetic zig-zag chains
We investigate the elementary excitations of quasi one-dimensional S=1/2
systems built up from zig-zag chains with general isotropic exchange constants,
using exact (Lanczos) diagonalization for 24 spins and series expansions
starting from the decoupled dimer limit. For the ideal one-dimensional zig-zag
chain we discuss the systematic variation of the basic (magnon) triplet
excitation with general exchange parameters and in particular the presence of
practically flat dispersions in certain regions of phase space. We extend the
dimer expansion in order to include the effects of 3D interactions on the
spectra of weakly interacting zig-zag chains. In an application to KCuCl_3 we
show that this approach allows to determine the exchange interactions between
individual pairs of spins from the spectra as determined in recent neutron
scattering experiments.Comment: 8 pages, 9 figures; some changes, figure added; final versio
International workshop AWA-PREFACE : "Socio economic impact of climate change in West Africa : insight from modeling and questionnaires" [résumés]
International audienc
Weakly supervised causal representation learning
Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however identifiable in a weakly supervised setting. This involves a dataset with paired samples before and after random, unknown interventions, but no further labels. We then introduce implicit latent causal models, variational autoencoders that represent causal variables and causal structure without having to optimize an explicit discrete graph structure. On simple image data, including a novel dataset of simulated robotic manipulation, we demonstrate that such models can reliably identify the causal structure and disentangle causal variables
Quantum phase transitions in the exactly solved spin-1/2 Heisenberg-Ising ladder
Ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with
the Heisenberg intra-rung and Ising inter-rung interactions is examined in
detail. The investigated model is transformed to the quantum Ising chain with
composite spins in an effective transverse and longitudinal field by employing
either the bond-state representation or the unitary transformation. It is shown
that the ground state of the Heisenberg-Ising ladder can be descended from
three exactly solvable models: the quantum Ising chain in a transverse field,
the 'classical' Ising chain in a longitudinal field or the spin-chain model in
a staggered longitudinal-transverse field. The last model serves in evidence of
the staggered bond phase with alternating singlet and triplet bonds on the
rungs of two-leg ladder, which appears at moderate values of the external
magnetic field and consequently leads to a fractional plateau at a half of the
saturation magnetization. The ground-state phase diagram totally consists of
five ordered and one quantum disordered phase, which are separated from each
other either by the lines of discontinuous or continuous quantum phase
transitions. The order parameters are exactly calculated for all five ordered
phases and the quantum disordered phase is characterized through different
short-range spin-spin correlations.Comment: corrected version, figure A1 has been changed, accepted in J. Phys.
A, 19 pages, 7 figure
Low Temperature Properties of Quantum Antiferromagnetic Chains with Alternating Spins S=1 and 1/2
We study the low-temperature properties of S=1 and 1/2 alternating spin
chains with antiferromagnetic nearest-neighbor exchange couplings using
analytical techniques as well as a quantum Monte Carlo method. The spin-wave
approach predicts two different low-lying excitations, which are gapped and
gapless, respectively. The structure of low-lying levels is also discussed by
perturbation theory in the strength of the Ising anisotropy. These analytical
findings are compared with the results of quantum Monte Carlo calculations and
it turns out that spin-wave theory well describes the present system. We
conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and
antiferromagnetic aspects.Comment: 13 pages, RevTeX, six figures, submitted to J. Phys. Cond. Ma
Thermodynamics of the (1,1/2) Ferrimagnet in Finite Magnetic Fields
We investigate the specific heat and magnetisation of a ferrimagnet with gS=1
and S=1/2 spins in a finite magnetic field using the transfer matrix DMRG down
to T=0.025J. Ferromagnetic gapless and antiferromagnetic gapped excitations for
H=0 lead to rich thermodynamics for H > 0. While the specific heat is
characterized by a generic double peak structure, magnetisation reveals two
critical fields, Hc1=1.76(1) and Hc2=3.00(1) with square-root behaviour in the
T=0 magnetisation. Simple analytical arguments allow to understand these
experimentally accessible findings.Comment: 5 pages, 7 eps figures, uses RevTeX, submitted to PR
Spin-dependent resonant tunneling through semimetallic ErAs quantum wells
Resonant tunneling through semimetallic ErAs quantum wells embedded in GaAs
structures with AlAs barriers was recently found to exhibit an intriguing
behavior in magnetic fields which is explained in terms of tunneling selection
rules and the spin-polarized band structure including spin-orbit coupling.Comment: 4 pages, figures supplied as self-unpacking figures.uu, uses
epsfig.sty to incorporate figures in preprin
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