66,849 research outputs found
Ground state properties of the bond alternating spin- anisotropic Heisenberg chain
Ground state properties, dispersion relations and scaling behaviour of spin
gap of a bond alternating spin- anisotropic Heisenberg chain have
been studied where the exchange interactions on alternate bonds are
ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The
resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM
bond alternating chains. Ground state energy has been estimated analytically by
using both bond operator and Jordan-Wigner representations and numerically by
using exact diagonalization. Dispersion relations, spin gap and several ground
state orders have been obtained. Dimer order and string orders are found to
coexist in the ground state. Spin gap is found to develop as soon as the
non-uniformity in alternating bond strength is introduced in the AFM-AFM chain
which further remains non-zero for the AFM-FM chain. This spin gap along with
the string orders attribute to the Haldane phase. The Haldane phase is found to
exist in most of the anisotropic region similar to the isotropic point.Comment: 16 pages, 6 figures, 1 tabl
Homoeopathy
Homoeopathy is a system of treating patients
using very low dose preparations according
to the principle: "like should be cured with
like". This paper summarises the research evidence
presented in a recent issue of Effective Health
Care on the effectiveness of homoeopathy.
Increasing numbers of patients are seeking
information on complementary medicines from
NHS health professionals. Results of a 1998 survey
of use and expenditure on complementary
medicine in England suggested that 28% of
respondents had either visited a complementary
therapist or had purchased an over the counter
herbal or homoeopathic remedy in the past year.
From this survey it was estimated that there
could be over 470 000 recent users of homoeopathic
remedies in England
Topological Defects on the Lattice I: The Ising model
In this paper and its sequel, we construct topologically invariant defects in
two-dimensional classical lattice models and quantum spin chains. We show how
defect lines commute with the transfer matrix/Hamiltonian when they obey the
defect commutation relations, cousins of the Yang-Baxter equation. These
relations and their solutions can be extended to allow defect lines to branch
and fuse, again with properties depending only on topology. In this part I, we
focus on the simplest example, the Ising model. We define lattice spin-flip and
duality defects and their branching, and prove they are topological. One useful
consequence is a simple implementation of Kramers-Wannier duality on the torus
and higher genus surfaces by using the fusion of duality defects. We use these
topological defects to do simple calculations that yield exact properties of
the conformal field theory describing the continuum limit. For example, the
shift in momentum quantization with duality-twisted boundary conditions yields
the conformal spin 1/16 of the chiral spin field. Even more strikingly, we
derive the modular transformation matrices explicitly and exactly.Comment: 45 pages, 9 figure
Stability of zero modes in parafermion chains
One-dimensional topological phases can host localized zero-energy modes that
enable high-fidelity storage and manipulation of quantum information. Majorana
fermion chains support a classic example of such a phase, having zero modes
that guarantee two-fold degeneracy in all eigenstates up to exponentially small
finite-size corrections. Chains of `parafermions'---generalized Majorana
fermions---also support localized zero modes, but, curiously, only under much
more restricted circumstances. We shed light on the enigmatic zero mode
stability in parafermion chains by analytically and numerically studying the
spectrum and developing an intuitive physical picture in terms of domain-wall
dynamics. Specifically, we show that even if the system resides in a gapped
topological phase with an exponentially accurate ground-state degeneracy,
higher-energy states can exhibit a splitting that scales as a power law with
system size---categorically ruling out exact localized zero modes. The
transition to power-law behavior is described by critical behavior appearing
exclusively within excited states.Comment: 15 pages, 8 figures; substantial improvements to chiral case,
coauthor added. Published 7 October 201
Consistent 3D Quantum Gravity on Lens Spaces
We study non-perturbative quantization of 3d gravity with positive
cosmological constant (de Sitter space being the prototype vacuum solution,
whose Euclideanization of course gives the three sphere) on the background
topology of lens space, which is a three spheres modulo a discrete group.
Instead of the strategy followed by a recent work \cite{Castro:2011xb}, which
compares results in the second and first order formulations of gravity, we
concentrate on the later solely. We note, as a striking feature, that the
quantization, that relies heavily on the axiomatics of topological quantum
field theory (TQFT) can only be consistently carried by augmenting the
conventional theory by an additional topological term coupled through a
dimensionless parameter. More importantly the introduction of this additional
parameter renders the theory finite.Comment: New section and references added. Accepted in Phys. Rev. D for
publicatio
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