782 research outputs found
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
Computing automorphic forms on Shimura curves over fields with arbitrary class number
We extend methods of Greenberg and the author to compute in the cohomology of
a Shimura curve defined over a totally real field with arbitrary class number.
Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke
eigenvalues associated to Hilbert modular forms of arbitrary level over a
totally real field of odd degree. We conclude with two examples which
illustrate the effectiveness of our algorithms.Comment: 15 pages; final submission to ANTS I
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
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
Random Hamiltonian in thermal equilibrium
A framework for the investigation of disordered quantum systems in thermal
equilibrium is proposed. The approach is based on a dynamical model--which
consists of a combination of a double-bracket gradient flow and a uniform
Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical
distribution. The resulting equilibrium state is used to calculate quenched and
annealed averages of quantum observables.Comment: 8 pages, 4 figures. To appear in DICE 2008 conference proceeding
Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
In this paper, I propose a technique for recovering quantum dynamical
information from imaginary-time data via the resolution of a one-dimensional
Hamburger moment problem. It is shown that the quantum autocorrelation
functions are uniquely determined by and can be reconstructed from their
sequence of derivatives at origin. A general class of reconstruction algorithms
is then identified, according to Theorem 3. The technique is advocated as
especially effective for a certain class of quantum problems in continuum
space, for which only a few moments are necessary. For such problems, it is
argued that the derivatives at origin can be evaluated by Monte Carlo
simulations via estimators of finite variances in the limit of an infinite
number of path variables. Finally, a maximum entropy inversion algorithm for
the Hamburger moment problem is utilized to compute the quantum rate of
reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.
Behavior of a frustrated quantum spin chain with bond dimerization
We clarified behavior of the excitation gap in a frustrated S=1/2 quantum
spin chain with bond dimerization by using the numerical diagonalization of
finite systems and a variational approach. The model interpolates between the
independent dimer model and the S=1 spin chain by changing a strength of the
dimerization. The energy gap is minimum at the fully-frustrated point, where a
localized kink and a freely mobile anti-kink govern the low-lying excitations.
Away from the point, a kink and an antikink form a bound state by an effective
triangular potential between them. The consequential gap enhancement and the
localization length of the bound state is obtained exactly in the continuous
limit. The gap enhancement obeys a power law with exponent 2/3. The method and
the obtained results are common to other frustrated double spin-chain systems,
such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.Comment: 11 pages, REVTeX, 8 figures in eps-fil
Quasi-periodic spin chains in a magnetic field
We study the interplay between a (quasi) periodic coupling array and an
external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization
plateaux are obtained by means of Abelian bosonization methods which give rise
to a sufficient quantization condition. The investigation of magnetic phase
diagrams via exact diagonalization of finite clusters finds a complete
agreement with the continuum treatment in a variety of situations.Comment: 4 pages RevTeX, 5 PostScript figures included. Final version to
appear in PR
Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet
The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed
inter-layer dimers is studied using quantum Monte Carlo simulations. A
zero-temperature multi-critical point (p*,g*) at the classical percolation
density p=p* and inter-layer coupling g* approximately 0.16 is demonstrated.
The quantum critical exponents of the percolating cluster are determined using
finite-size scaling. It is argued that the associated finite-temperature
quantum critical regime extends to zero inter-layer coupling and could be
relevant for antiferromagnetic cuprates doped with non-magnetic impurities.Comment: 4 pages, 6 figures. v2: only minor changes; accepted for publication
in Phys. Rev. Let
Numerical evaluation of one-loop QCD amplitudes
We present the publicly available program NGluon allowing the numerical
evaluation of primitive amplitudes at one-loop order in massless QCD. The
program allows the computation of one-loop amplitudes for an arbitrary number
of gluons. The focus of the present article is the extension to one-loop
amplitudes including an arbitrary number of massless quark pairs. We discuss in
detail the algorithmic differences to the pure gluonic case and present cross
checks to validate our implementation. The numerical accuracy is investigated
in detail.Comment: Talk given at ACAT 2011 conference in London, 5-9 Septembe
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