23,629 research outputs found
The spin 1/2 Heisenberg star with frustration II: The influence of the embedding medium
We investigate the spin 1/2 Heisenberg star introduced in J. Richter and A.
Voigt, J. Phys. A: Math. Gen. {\bf 27}, 1139 (1994). The model is defined by
; , . In extension to the Ref. we consider a more general
describing the properties of the spins surrounding the
central spin . The Heisenberg star may be considered as an essential
structure element of a lattice with frustration (namely a spin embedded in a
magnetic matrix ) or, alternatively, as a magnetic system with a
perturbation by an extra spin. We present some general features of the
eigenvalues, the eigenfunctions as well as the spin correlation of the model. For being a linear chain, a square
lattice or a Lieb-Mattis type system we present the ground state properties of
the model in dependence on the frustration parameter .
Furthermore the thermodynamic properties are calculated for being a
Lieb--Mattis antiferromagnet.Comment: 16 pages, uuencoded compressed postscript file, accepted to J. Phys.
A: Math. Ge
Localized-magnon states in strongly frustrated quantum spin lattices
Recent developments concerning localized-magnon eigenstates in strongly
frustrated spin lattices and their effect on the low-temperature physics of
these systems in high magnetic fields are reviewed. After illustrating the
construction and the properties of localized-magnon states we describe the
plateau and the jump in the magnetization process caused by these states.
Considering appropriate lattice deformations fitting to the localized magnons
we discuss a spin-Peierls instability in high magnetic fields related to these
states. Last but not least we consider the degeneracy of the localized-magnon
eigenstates and the related thermodynamics in high magnetic fields. In
particular, we discuss the low-temperature maximum in the isothermal entropy
versus field curve and the resulting enhanced magnetocaloric effect, which
allows efficient magnetic cooling from quite large temperatures down to very
low ones.Comment: 21 pages, 10 figures, invited paper for a special issue of "Low
Temperature Physics " dedicated to the 70-th anniversary of creation of
concept "antiferromagnetism" in physics of magnetis
Linear independence of localized magnon states
At the magnetic saturation field, certain frustrated lattices have a class of
states known as "localized multi-magnon states" as exact ground states. The
number of these states scales exponentially with the number of spins and
hence they have a finite entropy also in the thermodynamic limit
provided they are sufficiently linearly independent. In this article we present
rigorous results concerning the linear dependence or independence of localized
magnon states and investigate special examples. For large classes of spin
lattices including what we called the orthogonal type and the isolated type as
well as the kagom\'{e}, the checkerboard and the star lattice we have proven
linear independence of all localized multi-magnon states. On the other hand the
pyrochlore lattice provides an example of a spin lattice having localized
multi-magnon states with considerable linear dependence.Comment: 23 pages, 6 figure
Nonlinear projective filtering in a data stream
We introduce a modified algorithm to perform nonlinear filtering of a time
series by locally linear phase space projections. Unlike previous
implementations, the algorithm can be used not only for a posteriori processing
but includes the possibility to perform real time filtering in a data stream.
The data base that represents the phase space structure generated by the data
is updated dynamically. This also allows filtering of non-stationary signals
and dynamic parameter adjustment. We discuss exemplary applications, including
the real time extraction of the fetal electrocardiogram from abdominal
recordings.Comment: 8 page
Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
We consider the zero-temperature properties of the spin-half two-dimensional
Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method
(CCM) treatment. We find that this model demonstrates various groundstate
phases (N\'{e}el, magnetically disordered, orthogonal dimer), and we make
predictions for the positions of the phase transition points. In particular, we
find that orthogonal-dimer state becomes the groundstate at . For the critical point where the semi-classical N\'eel
order disappears we obtain a significantly lower value than ,
namely, in the range . We therefore conclude that
an intermediate phase exists between the \Neel and the dimer phases. An
analysis of the energy of a competing spiral phase yields clear evidence that
the spiral phase does not become the groundstate for any value of . The
intermediate phase is therefore magnetically disordered but may exhibit
plaquette or columnar dimer ordering.Comment: 6 pages, 5 figure
Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure
Using the coupled cluster method for high orders of approximation and Lanczos
exact diagonalization we study the ground-state phase diagram of a quantum
spin-1/2 J1-J2 model on the square lattice with plaquette structure. We
consider antiferromagnetic (J1>0) as well as ferromagnetic (J1<0)
nearest-neighbor interactions together with frustrating antiferromagnetic
next-nearest-neighbor interaction J2>0. The strength of inter-plaquette
interaction lambda varies between lambda=1 (that corresponds to the uniform
J1-J2 model) and lambda=0 (that corresponds to isolated frustrated 4-spin
plaquettes). While on the classical level (s \to \infty) both versions of
models (i.e., with ferro- and antiferromagnetic J1) exhibit the same
ground-state behavior, the ground-state phase diagram differs basically for the
quantum case s=1/2. For the antiferromagnetic case (J1 > 0) Neel
antiferromagnetic long-range order at small J2/J1 and lambda \gtrsim 0.47 as
well as collinear striped antiferromagnetic long-range order at large J2/J1 and
lambda \gtrsim 0.30 appear which correspond to their classical counterparts.
Both semi-classical magnetic phases are separated by a nonmagnetic quantum
paramagnetic phase. The parameter region, where this nonmagnetic phase exists,
increases with decreasing of lambda. For the ferromagnetic case (J1 < 0) we
have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of
J2 this classical phase gives way for a semi-classical plaquette phase, where
the plaquette block spins of length s=2 are antiferromagnetically long-range
ordered. Further increasing of J2 then yields collinear striped
antiferromagnetic long-range order for lambda \gtrsim 0.38, but a nonmagnetic
quantum paramagnetic phase lambda \lesssim 0.38.Comment: 10 pages, 15 figure
Quantum Phase Transitions in Spin Systems
We discuss the influence of strong quantum fluctuations on zero-temperature
phase transitions in a two-dimensional spin-half Heisenberg system. Using a
high-order coupled cluster treatment, we study competition of magnetic bonds
with and without frustration. We find that the coupled cluster treatment is
able to describe the zero-temperature transitions in a qualitatively correct
way, even if frustration is present and other methods such as quantum Monte
Carlo fail.Comment: 8 pages, 12 Postscipt figures; Accepted for publication in World
Scientifi
A solvable model of a random spin-1/2 XY chain
The paper presents exact calculations of thermodynamic quantities for the
spin-1/2 isotropic XY chain with random lorentzian intersite interaction and
transverse field that depends linearly on the surrounding intersite
interactions.Comment: 14 pages (Latex), 2 tables, 13 ps-figures included, (accepted for
publication in Phys.Rev.B
Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
We present a method for the direct calculation of the spin stiffness by means
of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on
the square, the triangular and the cubic lattices we calculate the stiffness in
high orders of approximation. For the square and the cubic lattices our results
are in very good agreement with the best results available in the literature.
For the triangular lattice our result is more precise than any other result
obtained so far by other approximate method.Comment: 5 pages, 2 figure
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