1,140 research outputs found
Isosbestic Points: Theory and Applications
We analyze the sharpness of crossing ("isosbestic") points of a family of
curves which are observed in many quantities described by a function f(x,p),
where x is a variable (e.g., the frequency) and p a parameter (e.g., the
temperature). We show that if a narrow crossing region is observed near x* for
a range of parameters p, then f(x,p) can be approximated by a perturbative
expression in p for a wide range of x. This allows us, e.g., to extract the
temperature dependence of several experimentally obtained quantities, such as
the Raman response of HgBa2CuO4+delta, photoemission spectra of thin VO2 films,
and the reflectivity of CaCu3Ti4O12, all of which exhibit narrow crossing
regions near certain frequencies. We also explain the sharpness of isosbestic
points in the optical conductivity of the Falicov-Kimball model and the
spectral function of the Hubbard model.Comment: 12 pages, 11 figure
Bound states in the one-dimensional two-particle Hubbard model with an impurity
We investigate bound states in the one-dimensional two-particle Bose-Hubbard
model with an attractive () impurity potential. This is a
one-dimensional, discrete analogy of the hydrogen negative ion H problem.
There are several different types of bound states in this system, each of which
appears in a specific region. For given , there exists a (positive) critical
value of , below which the ground state is a bound state.
Interestingly, close to the critical value (), the ground
state can be described by the Chandrasekhar-type variational wave function,
which was initially proposed for H. For , the ground state is no
longer a bound state. However, there exists a second (larger) critical value
of , above which a molecule-type bound state is established and
stabilized by the repulsion. We have also tried to solve for the eigenstates of
the model using the Bethe ansatz. The model possesses a global \Zz_2-symmetry
(parity) which allows classification of all eigenstates into even and odd ones.
It is found that all states with odd-parity have the Bethe form, but none of
the states in the even-parity sector. This allows us to identify analytically
two odd-parity bound states, which appear in the parameter regions
and , respectively. Remarkably, the latter one can be \textit{embedded}
in the continuum spectrum with appropriate parameters. Moreover, in part of
these regions, there exists an even-parity bound state accompanying the
corresponding odd-parity bound state with almost the same energy.Comment: 18 pages, 18 figure
Integrability and weak diffraction in a two-particle Bose-Hubbard model
A recently introduced one-dimensional two-particle Bose-Hubbard model with a
single impurity is studied on finite lattices. The model possesses a discrete
reflection symmetry and we demonstrate that all eigenstates odd under this
symmetry can be obtained with a generalized Bethe ansatz if periodic boundary
conditions are imposed. Furthermore, we provide numerical evidence that this
holds true for open boundary conditions as well. The model exhibits
backscattering at the impurity site -- which usually destroys integrability --
yet there exists an integrable subspace. We investigate the non-integrable even
sector numerically and find a class of states which have almost the Bethe
ansatz form. These weakly diffractive states correspond to a weak violation of
the non-local Yang-Baxter relation which is satisfied in the odd sector. We
bring up a method based on the Prony algorithm to check whether a numerically
obtained wave function is in the Bethe form or not, and if so, to extract
parameters from it. This technique is applicable to a wide variety of other
lattice models.Comment: 13.5 pages, 11 figure
Non-perturbative approaches to magnetism in strongly correlated electron systems
The microscopic basis for the stability of itinerant ferromagnetism in
correlated electron systems is examined. To this end several routes to
ferromagnetism are explored, using both rigorous methods valid in arbitrary
spatial dimensions, as well as Quantum Monte Carlo investigations in the limit
of infinite dimensions (dynamical mean-field theory). In particular we discuss
the qualitative and quantitative importance of (i) the direct Heisenberg
exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a
high spectral density near the band edges caused by an appropriate lattice
structure and/or kinetic energy of the electrons. We furnish evidence of the
stability of itinerant ferromagnetism in the pure Hubbard model for appropriate
lattices at electronic densities not too close to half-filling and large enough
. Already a weak direct exchange interaction, as well as band degeneracy, is
found to reduce the critical value of above which ferromagnetism becomes
stable considerably. Using similar numerical techniques the Hubbard model with
an easy axis is studied to explain metamagnetism in strongly anisotropic
antiferromagnets from a unifying microscopic point of view.Comment: 11 pages, Latex, and 6 postscript figures; Z. Phys. B, in pres
Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity
We report a bound state of the one-dimensional two-particle (bosonic or
fermionic) Hubbard model with an impurity potential. This state has the
Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide
region in parameter space, its energy is located in the continuum band. A
remarkable advantage of this state with respect to similar states in other
systems is the simple analytical form of the wave function and eigenvalue. This
state can be tuned in and out of the continuum continuously.Comment: A semi-exactly solvable model (half of the eigenstates are in the
Bethe form
Autocompensative System for Measurement of the Capacitances
A simple and successful design of an autocompensative system with flip-flop sensor for measurement of capacitances is presented. The analysis of the sensor is based on the state description with the vertical rise segments of the control pulse. The theoretical results are compared with measured data and good agreement is reported
Phase separation in the particle-hole asymmetric Hubbard model
The paramagnetic phase diagram of the Hubbard model with nearest-neighbor
(NN) and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed
at half-filling and in the weakly doped regime using the self-energy functional
approach for dynamical mean-field theory. NNN hopping breaks the particle-hole
symmetry and leads to a strong asymmetry of the electron-doped and hole-doped
regimes. Phase separation occurs at and near half-filling, and the critical
temperature of the Mott transition is strongly suppressed.Comment: 8 pages, 8 figure
What are spin currents in Heisenberg magnets?
We discuss the proper definition of the spin current operator in Heisenberg
magnets subject to inhomogeneous magnetic fields. We argue that only the
component of the naive "current operator" J_ij S_i x S_j in the plane spanned
by the local order parameters and is related to real transport of
magnetization. Within a mean field approximation or in the classical ground
state the spin current therefore vanishes. Thus, finite spin currents are a
direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio
Telescopic actions
A group action H on X is called "telescopic" if for any finitely presented
group G, there exists a subgroup H' in H such that G is isomorphic to the
fundamental group of X/H'.
We construct examples of telescopic actions on some CAT[-1] spaces, in
particular on 3 and 4-dimensional hyperbolic spaces. As applications we give
new proofs of the following statements:
(1) Aitchison's theorem: Every finitely presented group G can appear as the
fundamental group of M/J, where M is a compact 3-manifold and J is an
involution which has only isolated fixed points;
(2) Taubes' theorem: Every finitely presented group G can appear as the
fundamental group of a compact complex 3-manifold.Comment: +higher dimension
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