1,283 research outputs found
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
Thermodynamical Properties of a Spin 1/2 Heisenberg Chain Coupled to Phonons
We performed a finite-temperature quantum Monte Carlo simulation of the
one-dimensional spin-1/2 Heisenberg model with nearest-neighbor interaction
coupled to Einstein phonons. Our method allows to treat easily up to 100
phonons per site and the results presented are practically free from truncation
errors. We studied in detail the magnetic susceptibility, the specific heat,
the phonon occupation, the dimerization, and the spin-correlation function for
various spin-phonon couplings and phonon frequencies. In particular we give
evidence for the transition from a gapless to a massive phase by studying the
finite-size behavior of the susceptibility. We also show that the dimerization
is proportional to for .Comment: 10 pages, 17 Postscript Figure
On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals
The dynamic and kinetic behavior of processes occurring in fractals with
spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the
existence of a fundamental scaling ratio (b_1). We address time-dependent
physical processes, which as a consequence of the time evolution develop a
characteristic length of the form , where z is the dynamic
exponent. So, we conjecture that the interplay between the physical process and
the symmetry properties of the fractal leads to the occurrence of time DSI
evidenced by soft log-periodic modulations of physical observables, with a
fundamental time scaling ratio given by . The conjecture is
tested numerically for random walks, and representative systems of broad
universality classes in the fields of irreversible and equilibrium critical
phenomena.Comment: 6 pages, 3 figures. Submitted to EP
Spectrum and transition rates of the XX chain analyzed via Bethe ansatz
As part of a study that investigates the dynamics of the s=1/2 XXZ model in
the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz
equations for the case Delta=0 (XX model). We identify the general structure of
the Bethe ansatz solutions for the entire XX spectrum, which include states
with real and complex magnon momenta. We discuss the relation between the
spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions
(Jordan-Wigner representation). We present determinantal expressions for
transition rates of spin fluctuation operators between Bethe wave functions and
reduce them to product expressions. We apply the new formulas to two-spinon
transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure
Fusion Operators in the Generalized -model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
We construct the fusion operators in the generalized -model using
the fused -operators, and verify the fusion relations with the truncation
identity. The algebraic Bethe ansatz discussion is conducted on two special
classes of which include the superintegrable chiral Potts model.
We then perform the parallel discussion on the XXZ spin chain at roots of
unity, and demonstrate that the -loop-algebra symmetry exists for the
root-of-unity XXZ spin chain with a higher spin, where the evaluation
parameters for the symmetry algebra are identified by the explicit
Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the
comparison with the superintegrable chiral Potts model.Comment: Latex 33 Pages; Typos and errors corrected, New improved version by
adding explanations for better presentation. Terminology in the content and
the title refined. References added and updated-Journal versio
Dwarf Galaxy Dark Matter Density Profiles Inferred from Stellar and Gas Kinematics
We present new constraints on the density profiles of dark matter (DM) halos
in seven nearby dwarf galaxies from measurements of their integrated stellar
light and gas kinematics. The gas kinematics of low mass galaxies frequently
suggest that they contain constant density DM cores, while N-body simulations
instead predict a cuspy profile. We present a data set of high resolution
integral field spectroscopy on seven galaxies and measure the stellar and gas
kinematics simultaneously. Using Jeans modeling on our full sample, we examine
whether gas kinematics in general produce shallower density profiles than are
derived from the stars. Although 2/7 galaxies show some localized differences
in their rotation curves between the two tracers, estimates of the central
logarithmic slope of the DM density profile, gamma, are generally robust. The
mean and standard deviation of the logarithmic slope for the population are
gamma=0.67+/-0.10 when measured in the stars and gamma=0.58+/-0.24 when
measured in the gas. We also find that the halos are not under concentrated at
the radii of half their maximum velocities. Finally, we search for correlations
of the DM density profile with stellar velocity anisotropy and other baryonic
properties. Two popular mechanisms to explain cored DM halos are an exotic DM
component or feedback models that strongly couple the energy of supernovae into
repeatedly driving out gas and dynamically heating the DM halos. We investigate
correlations that may eventually be used to test models. We do not find a
secondary parameter that strongly correlates with the central DM density slope,
but we do find some weak correlations. Determining the importance of these
correlations will require further model developments and larger observational
samples. (Abridged)Comment: 29 pages, 18 figures, 10 tables, accepted for publication in Ap
The KMOS^3D Survey: design, first results, and the evolution of galaxy kinematics from 0.7<z<2.7
We present the KMOS^3D survey, a new integral field survey of over 600
galaxies at 0.7<z<2.7 using KMOS at the Very Large Telescope (VLT). The KMOS^3D
survey utilizes synergies with multi-wavelength ground and space-based surveys
to trace the evolution of spatially-resolved kinematics and star formation from
a homogeneous sample over 5 Gyrs of cosmic history. Targets, drawn from a
mass-selected parent sample from the 3D-HST survey, cover the star
formation-stellar mass () and rest-frame planes uniformly. We
describe the selection of targets, the observations, and the data reduction. In
the first year of data we detect Halpha emission in 191
Msun galaxies at z=0.7-1.1 and z=1.9-2.7. In
the current sample 83% of the resolved galaxies are rotation-dominated,
determined from a continuous velocity gradient and , implying
that the star-forming 'main sequence' (MS) is primarily composed of rotating
galaxies at both redshift regimes. When considering additional stricter
criteria, the Halpha kinematic maps indicate at least ~70% of the resolved
galaxies are disk-like systems. Our high-quality KMOS data confirm the elevated
velocity dispersions reported in previous IFS studies at z>0.7. For
rotation-dominated disks, the average intrinsic velocity dispersion decreases
by a factor of two from 50 km/s at z~2.3 to 25 km/s at z~0.9 while the
rotational velocities at the two redshifts are comparable. Combined with
existing results spanning z~0-3, disk velocity dispersions follow an
approximate (1+z) evolution that is consistent with the dependence of velocity
dispersion on gas fractions predicted by marginally-stable disk theory.Comment: 20 pages, 11 figures, 1 Appendix; Accepted to ApJ November 2
Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
The construction of auxiliary matrices for the six-vertex model at a root of
unity is investigated from a quantum group theoretic point of view. Employing
the concept of intertwiners associated with the quantum loop algebra
at a three parameter family of auxiliary matrices
is constructed. The elements of this family satisfy a functional relation with
the transfer matrix allowing one to solve the eigenvalue problem of the model
and to derive the Bethe ansatz equations. This functional relation is obtained
from the decomposition of a tensor product of evaluation representations and
involves auxiliary matrices with different parameters. Because of this
dependence on additional parameters the auxiliary matrices break in general the
finite symmetries of the six-vertex model, such as spin-reversal or spin
conservation. More importantly, they also lift the extra degeneracies of the
transfer matrix due to the loop symmetry present at rational coupling values.
The extra parameters in the auxiliary matrices are shown to be directly related
to the elements in the enlarged center of the quantum loop algebra
at . This connection provides a geometric
interpretation of the enhanced symmetry of the six-vertex model at rational
coupling. The parameters labelling the auxiliary matrices can be interpreted as
coordinates on a three-dimensional complex hypersurface which remains invariant
under the action of an infinite-dimensional group of analytic transformations,
called the quantum coadjoint action.Comment: 52 pages, TCI LaTex, v2: equation (167) corrected, two references
adde
Line shapes of dynamical correlation functions in Heisenberg chains
We calculate line shapes of correlation functions by use of complete
diagonalization data of finite chains and analytical implications from
conformal field theory, density of states, and Bethe ansatz. The numerical data
have different finite size accuracy in case of the imaginary and real parts in
the frequency and time representations of spin-correlation functions,
respectively. The low temperature, conformally invariant regime crosses over at
to a diffusive regime that in turn connects continuously to
the high temperature, interacting fermion regime. The first moment sum rule is
determined.Comment: 13 pages REVTEX, 18 figure
Dynamical correlation functions of the XXZ model at finite temperature
Combining a lattice path integral formulation for thermodynamics with the
solution of the quantum inverse scattering problem for local spin operators, we
derive a multiple integral representation for the time-dependent longitudinal
correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature
and in an external magnetic field. Our formula reproduces the previous results
in the following three limits: the static, the zero-temperature and the XY
limits.Comment: 22 pages, v4: typos corrected, published versio
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