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 $H=J_1 \sum_{i=1}^{N}{{\bf s}_0{\bf s}_i} + J_2 H_{R}\{{\bf s}_i\}$ ; $J_1,J_2 \ge 0$ , $i=1,...,N$. In extension to the Ref. we consider a more general $H_{R}\{{\bf s}_i\}$ describing the properties of the spins surrounding the central spin ${\bf s}_0$. The Heisenberg star may be considered as an essential structure element of a lattice with frustration (namely a spin embedded in a magnetic matrix $H_R$) or, alternatively, as a magnetic system $H_R$ with a perturbation by an extra spin. We present some general features of the eigenvalues, the eigenfunctions as well as the spin correlation $\langle {\bf s}_0{\bf s}_i \rangle$ of the model. For $H_R$ 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 $\alpha=J_2/J_1$. Furthermore the thermodynamic properties are calculated for $H_R$ 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 $N$ of spins and hence they have a finite entropy also in the thermodynamic limit $N\to \infty$ 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 ${J}^{d}_2/J_1 \sim 1.477$. For the critical point $J_2^{c}/J_1$ where the semi-classical N\'eel order disappears we obtain a significantly lower value than $J_2^{d}/J_1$, namely, ${J}^{c}_2/J_1$ in the range $[1.14, 1.39]$. 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 $J_2$. 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