1,161 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
Phase diagram of an exactly solvable t-J ladder model
We study a system of one-dimensional t-J models coupled to a ladder system. A
special choice of the interaction between neighbouring rungs leads to an
integrable model with supersymmetry, which is broken by the presence of rung
interactions. We analyze the spectrum of low-lying excitations and ground state
phase diagram at zero temperature.Comment: LaTeX, 8 pp. incl. 1 figur
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
Electronic Ladders with SO(5) Symmetry: Phase Diagrams and Correlations at half-filling
We construct a family of electronic ladder models with SO(5) symmetry which
have exact ground states in the form of finitely correlated wave functions.
Extensions for these models preserving this symmetry are studied using these
states in a variational approach. Within this approach, the zero temperature
phase diagram of these electronic ladders at half filling is obtained,
reproducing the known results in the weak coupling (band insulator) and strong
coupling regime, first studied by Scalapino, Zhang and Hanke. Finally, the
compact form of the variational wave functions allows to compute various
correlation functions for these systems.Comment: RevTeX+epsf macros, 23 pp. including figure
Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice
Within the zero-temperature linear spin-wave theory we have investigated the
effect of frustration and dimerization of a Heisenberg system with alternating
spins and on one- and two-dimensional lattices. The combined
effect most visibly appears in the elementary excitation spectra. In contrast
to the ground state energy that decreases with dimerization and increases with
frustration, the excitation energies are shown to be suppressed in energy by
both dimerization and frustration. The threshold value of frustration that
signals a transition from a classical ferrimagnetic state to a spiral state,
decreases with dimerization, showing that dimerization further helps in the
phase transition. The correlation length and sublattice magnetization decrease
with both dimerization and frustration indicating the destruction of the
long-range classical ferrimagnetic. The linear spin wave theory shows that in
the case of a square lattice, dimerization initially opposes the
frustration-led transition to a spiral magnetic state, but then higher
magnitudes of lattice deformation facilitate the transition. It also shows that
the transition to spiral state is inhibited in a square lattice beyond a
certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure
An application of the natural area concept to East London apartment areas
The world is faced with a population explosion, and cities are becoming ever larger. The world population will grow from its present 3500 million to more than 7 000 million by the year 2 000. The majority of cities are thus faced with the problem of housing vast numbers of people living in single family dwellings forming low density urban sprawl. Conditions are no different in South Africa where the present white population of about four million is expected to grow to between six and seven million by the year 2000. The present housing requirement (1970-75) for Whites, based on low and high population projections, is 32 732 and 40 150 houses respectively. From 1995-2000 the figures will have risen to 42 742 and 65 580 respectively. At that rate sprawl here will reach alarming proportions unless it can be curtailed by higher density housing. As the population trend does not seem likely to be reversed the problem lies in how to provide housing for an escalating population but at the same time to reduce urban sprawl and provide satisfactory living conditions
Functional Liftings of Vectorial Variational Problems with Laplacian Regularization
We propose a functional lifting-based convex relaxation of variational
problems with Laplacian-based second-order regularization. The approach rests
on ideas from the calibration method as well as from sublabel-accurate
continuous multilabeling approaches, and makes these approaches amenable for
variational problems with vectorial data and higher-order regularization, as is
common in image processing applications. We motivate the approach in the
function space setting and prove that, in the special case of absolute
Laplacian regularization, it encompasses the discretization-first
sublabel-accurate continuous multilabeling approach as a special case. We
present a mathematical connection between the lifted and original functional
and discuss possible interpretations of minimizers in the lifted function
space. Finally, we exemplarily apply the proposed approach to 2D image
registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and
Variational Methods" in Hofgeismar, Germany 201
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
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
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