1,601 research outputs found
Horizontal variation of Tate--Shafarevich groups
Let be an elliptic curve over . Let be an odd prime and
an embedding. Let
be an imaginary quadratic field and the corresponding Hilbert class
field. For a class group character over , let be
the field generated by the image of and the prime
of above determined via . Under mild
hypotheses, we show that the number of class group characters such that
the -isotypic Tate--Shafarevich group of over is finite with
trivial -part increases with the absolute value of the
discriminant of
Magnetization plateaus in antiferromagnetic-(ferromagnetic)_{n} polymerized S=1/2 XXZ chains
The plateau-non-plateau transition in the
antiferromagnetic-(ferromagnetic) polymerized XXZ chains under
the magnetic field is investigated. The universality class of this transition
belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points
are determined by level spectroscopy analysis of the numerical diagonalization
data for where is the size of a unit cell.
It is found that the critical strength of ferromagnetic coupling decreases with
for small but increases for larger enough . It is also found that
the plateau for large is wide enough for moderate values of exchange
coupling so that it should be easily observed experimentally. This is in
contrast to the plateaus for chains which are narrow for a wide range
of exchange coupling even away from the critical point
Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets
It is conjectured that the Haldane phase of the S=1 antiferromagnetic
Heisenberg chain and the ferromagnetic-antiferromagnetic alternating
Heisenberg chain is stable against any strength of randomness, because of
imposed breakdown of translational symmetry. This conjecture is confirmed by
the density matrix renormalization group calculation of the string order
parameter and the energy gap distribution.Comment: 4 Pages, 7 figures; Considerable revisions are made in abstract and
main text. Final accepted versio
Quantum disorder due to singlet formation: The Plaquette lattice
I study the order/disorder transition due to singlet formation in a quantum
spin system by means of exact diagonalization. The systems is build by spin 1/2
on a two-dimensional square lattice with two different kinds of
antiferromagnetic Heisenberg interactions. The interaction J_p connects 4
nearest neighbor spins on a plaquette. The interaction J_n connects the
plaquettes with each other. If J_p=J_n the systems reduces to the simple square
lattice case. If one of the interactions becomes sufficiently larger then the
other the purely quantum effect of singlet formation drives the system into a
disordered phase with only short range correlations in the plaquettes and a
spin gap. I study the transition point by evaluating the spin gap and spin-spin
correlations. I compare the results with previously calculated data from a
non-linear sigma model approach, spin wave theory and series expansion
calculations. I confirm a critical value of J_n \approx 0.6 for the quantum
phase transition point.Comment: 5 pages (Revtex), 7 figure
Extensions of abelian varieties defined over a number field
We study the arithmetic aspects of the finite group of extensions of abelian
varieties defined over a number field. In particular, we establish relations
with special values of L-functions and congruences between modular forms.Comment: 11 page
Quantum Antiferromagnetism in Quasicrystals
The antiferromagnetic Heisenberg model is studied on a two-dimensional
bipartite quasiperiodic lattice. The distribution of local staggered magnetic
moments is determined on finite square approximants with up to 1393 sites,
using the Stochastic Series Expansion Quantum Monte Carlo method. A non-trivial
inhomogeneous ground state is found. For a given local coordination number, the
values of the magnetic moments are spread out, reflecting the fact that no two
sites in a quasicrystal are identical. A hierarchical structure in the values
of the moments is observed which arises from the self-similarity of the
quasiperiodic lattice. Furthermore, the computed spin structure factor shows
antiferromagnetic modulations that can be measured in neutron scattering and
nuclear magnetic resonance experiments.
This generic model is a first step towards understanding magnetic
quasicrystals such as the recently discovered Zn-Mg-Ho icosahedral structure.Comment: RevTex, 4 pages with 5 figure
The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3
A possibility of the uniform antiferromagnetic order is pointed out in an
S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg
quantum spin chain compound: (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3. The system
possesses the bond alternation of strong random bonds that take +/- 2J and weak
uniform AF bonds of -J. In the pure concentration limits, the model reduces to
the AF-AF alternation chain at x=0 and to the F-AF alternation chain at x=1.
The nonequilibrium relaxation of large-scale quantum Monte Carlo simulations
exhibits critical behaviors of the uniform AF order in the intermediate
concentration region, which explains the experimental observation of the
magnetic phase transition. The present results suggest that the uniform AF
order may survive even in the presence of the randomly located ferromagnetic
bonds.Comment: 4 pages, 3 figure
Entanglement Generation by Qubit Scattering in Three Dimensions
A qubit (a spin-1/2 particle) prepared in the up state is scattered by local
spin-flipping potentials produced by the two target qubits (two fixed spins),
both prepared in the down state, to generate an entangled state in the latter
when the former is found in the down state after scattering. The scattering
process is analyzed in three dimensions, both to lowest order and in full order
in perturbation, with an appropriate renormalization for the latter. The
entanglement is evaluated in terms of the concurrence as a function of the
incident and scattering angles, the size of the incident wave packet, and the
detector resolution, to clarify the key elements for obtaining an entanglement
with high quality. The characteristics of the results are also discussed in the
context of (in)distinguishability of alternative paths for a quantum particle.Comment: 21 pages, 19 figures, the final versio
Ground State and Magnetization Process of the Mixture of Bond-Alternating and Uniform S=1/2 Antiferromagnetic Heisenberg Chains
The mixture of bond-alternating and uniform S=1/2 antiferromagnetic
Heisenberg chains is investigated by the density matrix renormalization group
method. The ground state magnetization curve is calculated and the exchange
parameters are determined by fitting to the experimentally measured
magnetization curve of \CuClBr(-pic). The low
field behavior of the magnetization curve and low temperature behavior of the
magnetic susceptibility are found to be sensitive to whether the
bond-alternation pattern (parity) is fixed all over the sample or randomly
distributed. The both quantities are compatible with the numerical results for
the random parity model.Comment: 5 pages, 7 figures. Final and enlarged version accepted for
publication in J. Phys. Soc. Jp
Effects of Single-site Anisotropy on Mixed Diamond Chains with Spins 1 and 1/2
Effects of single-site anisotropy on mixed diamond chains with spins 1 and
1/2 are investigated in the ground states and at finite temperatures. There are
phases where the ground state is a spin cluster solid, i.e., an array of
uncorrelated spin-1 clusters separated by singlet dimers. The ground state is
nonmagnetic for the easy-plane anisotropy, while it is paramagnetic for the
easy-axis anisotropy. Also, there are the N\'eel, Haldane, and large-
phases, where the ground state is a single spin cluster of infinite size and
the system is equivalent to the spin-1 Heisenberg chain with alternating
anisotropy. The longitudinal and transverse susceptibilities and entropy are
calculated at finite temperatures in the spin-cluster-solid phases. Their
low-temperature behaviors are sensitive to anisotropy.Comment: 8 pages, 4 figure
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