87 research outputs found
Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings
We suggest a general rule for the shift quantum numbers k of the relative
ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes
well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even
rings. Our rule is confirmed by numerical investigations and rigorous proofs
for special cases, including systems with a Haldane gap. Implications for the
total spin quantum number S of relative ground states are discussed as well as
generalizations to the XXZ model.Comment: 8 pages, 2 figures, submitted to Phys. Rev. B. More information at
http://www.physik.uni-osnabrueck.de/makrosysteme
Ground state properties of antiferromagnetic Heisenberg spin rings
Exact ground state properties of antiferromagnetic Heisenberg spin rings with
isotropic next neighbour interaction are presented for various numbers of spin
sites and spin quantum numbers. Earlier work by Peierls, Marshall, Lieb,
Schultz and Mattis focused on bipartite lattices and is not applicable to rings
with an odd number of spins. With the help of exact diagonalization methods we
find a more general systematic behaviour which for instance relates the number
of spin sites and the individual spin quantum numbers to the degeneracy of the
ground state. These numerical findings all comply with rigorous proofs in the
cases where a general analysis could be carried out. Therefore it can be
plausibly conjectured that the ascertained properties hold for ground states of
arbitrary antiferromagnetic Heisenberg spin rings.Comment: 13 pages, 5 figures, uses epsfig.sty, submitted to Phys. Rev. B. More
information at http://www.physik.uni-osnabrueck.de/makrosysteme
Transition from diffusive to ballistic dynamics for a class of finite quantum models
The transport of excitation probabilities amongst weakly coupled subunits is
investigated for a class of finite quantum systems. It is demonstrated that the
dynamical behavior of the transported quantity depends on the considered length
scale, e. g., the introduced distinction between diffusive and ballistic
transport appears to be a scale-dependent concept, especially since a
transition from diffusive to ballistic behavior is found in the limit of small
as well as in the limit of large length scales. All these results are derived
by an application of the time-convolutionless projection operator technique and
are verified by the numerical solution of the full time-dependent Schroedinger
equation which is obtained by exact diagonalization for a range of model
parameters.Comment: 4 pages, 5 figures, approved for publication in Physical Review
Letter
Retarded versus time-nonlocal quantum kinetic equations
The finite duration of the collisions in Fermionic systems as expressed by
the retardation time in non-Markovian Levinson-type kinetic equations is
discussed in the quasiclassical limit. We separate individual contributions
included in the memory effect resulting in (i) off-shell tails of the Wigner
distribution, (ii) renormalization of scattering rates and (iii) of the
single-particle energy, (iv) collision delay and (v) related non-local
corrections to the scattering integral. In this way we transform the Levinson
equation into the Landau-Silin equation extended by the non-local corrections
known from the theory of dense gases. The derived nonlocal kinetic equation
unifies the Landau theory of quasiparticle transport with the classical kinetic
theory of dense gases. The space-time symmetry is discussed versus
particle-hole symmetry and a solution is proposed which transforms these two
exclusive pictures into each other.Comment: slightly revised, 19 page
Quantum entanglement and Bell inequalities in Heisenberg spin chains
We show that in one-dimensional isotropic Heisenberg model two-qubit thermal
entanglement and maximal violation of Bell inequalities are directly related
with a thermodynamical state function, i.e., the internal energy. Therefore
they are completely determined by the partition function, the central object of
thermodynamics. For ferromagnetic ring we prove that there is no thermal
entanglement at any temperature. Explicit relations between the concurrence and
the measure of maximal Bell inequality violation are given.Comment: 4 pages, no figure
A simple model for magnetism in itinerant electron systems
A new lattice model of interacting electrons is presented. It can be viewed
as a classical Hubbard model in which the energy associated to electron
itinerance is proportional to the total number of possible electron jumps.
Symmetry properties of the Hubbard model are preserved. In the half-filled band
with strong interaction the model becomes the Ising model. The main features of
the magnetic behavior of the model in the one-dimensional and mean-field cases
are studied.Comment: 9 pages, 3 figures, to be published in Physica
The concept of correlated density and its application
The correlated density appears in many physical systems ranging from dense
interacting gases up to Fermi liquids which develop a coherent state at low
temperatures, the superconductivity. One consequence of the correlated density
is the Bernoulli potential in superconductors which compensates forces from
dielectric currents. This Bernoulli potential allows to access material
parameters. Though within the surface potential these contributions are largely
canceled, the bulk measurements with NMR can access this potential. Recent
experiments are explained and new ones suggested. The underlying quantum
statistical theory in nonequilibrium is the nonlocal kinetic theory developed
earlier.Comment: 14 pages, CMT30 proceeding
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