Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation 〈S ₀ S _r 〉 decreases asymptotically asr ^?1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this “superfrustration” on the free energy and on the ground state properties is also discussed.     

Ground state phase diagrams for the mixed Ising 3/2 and 5/2 spin model

We calculate the ground state phase diagrams of a mixed Ising model on a square lattice where spins S (± 3/2, ± 1/2) in one sublattice are in alternating sites with spins Q (± 5/2, ± 3/2, ± 1/2), located on the other sublattice. The Hamiltonian of the model includes first neighbor interactions between the S and Q spins, next-nearest-neighbor interactions between the S spins, and between the Q spins, and crystal field. The topologies of the phase diagrams depend on the values of the parameters in the Hamiltonian. The diagrams show some key features: coexistence between regions, points where two, three, four, five and six states can coexist. Besides being very useful as a way to check the low temperature limit of the finite-temperature phase diagram, often obtained by mean-field theories, the richness of the ground state diagrams for certain combinations of parameters can be used as a guide to explore interesting regions of the finite-temperature phase diagram of the model.     

Spin correlations of inhomogeneous valence bond solid chains

We consider a spacially inhomogeneous generalization of the valence bond solid (VBS) chain by permitting an arbitrary distribution of the numbers of valence bonds. We evaluate all two point correlation functions of these VBS states. The correlation functions turn out to factorize completely into a product of local factors. This leads to very simple rules for their evaluation and implies the breaking of correlations of higher rank by a single weak link.Research performed within the program of the Sonderforschungsbereich 341 supported by the Deutsche Forschungsgemeinschaft     

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension . This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to . NSF Grant DMS-0503712.     

Triplet-singlet interaction in the 1s 2s3S1 hyperfine splitting of he-like Li+

The hyperfine structure (hfs) interaction between the metastable 2³ S ₁ and 2¹ S ₀ states in^{6, 7}Li⁺ causes very small equal and opposite energy level shifts,δ, in the two levels having the same total angular momentum quantum numberF=I. This amounts to 12ppm with respect to the total hfs splitting of 30 GHz for the⁷Li⁺ 2³S₁ state and has been measured for the first time directly for the case of a core-free electronic system by combined laser-microwave spectroscopy. A new calculation ofδ with accurate integral-transform 2¹ S ₀ and 2³S₁ wave functions is reported. Configuration interactions and electron exchange and correlation effects, which differ for parallel (³ S ₁) and antiparallel (¹ S ⁰) spins, are treated in detail in order to obtain very good agreement between measured and theoretical values for this tiny perturbation. A complete understanding ofδ is indispensable for extracting fundamental constants from two-electron spectroscopic data.     

Haldane-like antiferromagnetic spin chain in the large anisotropy limit

We consider the one dimensional, periodic spin chain with N sites, similar to the one studied by Haldane [1], however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude s. For a chain with an even number of sites we show that actually the ground state is non-degenerate and given by a superposition of the two Neél states, due to quantum spin tunnelling. With an odd number of sites, the Neél state must necessarily contain a soliton. The position of the soliton is arbitrary thus the ground state is N-fold degenerate. This set of states reorganizes into a band. We show that this occurs at order 2s in perturbation theory. The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramers' theorem [18].     

Quantum and Classical Correlations in the Solid-State NMR Free Induction Decay

The free induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spin ones coincide if there are many nearly equivalent nearest neighbors n in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S > 1/2 we provide generalized POVM measurement (positive-operator-valued measure) using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S + 1) when S is growing up, and quantum properties disappear completely only if S → ∞.     

Numerische Berechnung von Spin-Korrelationsfunktionen und Magnetisierungskurven von Ferromagnetica

The static correlation functions and the magnetization curves of finite (125–1000 spins) Ising- and Heisenberg-ferromagnets are calculated using a Monte-Carlomethod for all temperatures. We assumeS=∞, a simple cubic lattice and nearest neighbours interactions. Various theoretical assumptions concerning the correlation functions and the magnetization may be examined by means of the calculated results. Magnetization curves for superparamagnetic systems were computed also.     

Two-dimensional decorated Ising model with classical vector spins and Ising spins of magnitude s

A two-dimensional decorated Ising model with ν-dimensional vector spins and Ising spins of magnitude s is considered. The partition function, magnetization and correlation functions are expressed in terms of the average of functions of the spins of the Ising model with effective exchange constants. These results, although derived for a two-dimensional lattice, are valid for a lattice of arbitrary dimensionality. The phase diagram is obtained exactly in the zero external field and two-dimensional lattice for arbitrary values of s and ν, and, as expected, three transition temperatures are obtained for some values of the parameters. It is also shown that for $\text{|}\text{S}\text{|=1, s>}\text{1}\text{2}$ there is an additional ordered phase (up-down/up-down), and for $\text{|}\text{S}\text{|=ν}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ this additional phase can be either up-down/up-down or up-up/down-down depending on the values of ν and s.     

Heisenberg-antiferromagnet and loop-soup

An analytic approximation to the loop-soup approach of Liang et al. to the spin 1/2 Heisenberg antiferromagnet is introduced. It allows for a staggered long-range correlation of the spins ind>1 dimensions. The wavevector-dependence for the static spin-correlation function and for the averaged spinwave-energy agrees qualitatively with that obtained in spinwave approximation. Since my approximation does not exclude the intersection of loops, the expectation value of the spin-spin correlation at short distances is larger by a factor of approximately 3/2, similarly as in the Boson mean-field approximation. The elementary bosonic excitations of this theory correspond in my case to single unpaired spins moving on one sublattice through the system with (apart from a different overall prefactor) the same dispersion. Within the present approach the amplitudesh of the singlets in the wave function fall off liker ^–d–1 for pairs of spins a distancer apart, if long-range order is present. This suggests that the loop-soup picture may be a good starting point for further investigations.Work supported in part by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 123 Stochastic Mathematical Models     

Comments on the presence of a peak in the static structure factor of an electron liquid

Emphasis is laid on the fact that the peak in the static structure factor S(k) observed in a recent experiment at k≈2k_F for conduction electrons in beryllium agrees well with the one predicted by us theoretically some time back. The error in the calculation of the pair correlation function g(r) using the experimental data on S(k) is pointed out. The position of the peak obtained in our g(r) clearly indicates that the effect of electron correlation is to condense into a Wigner lattice at a distance equal to the average interparticle separation rather than making a Mott type transition to an atomic-like state.     

Determination of the amplitudes and phases of the scattering matrix upon photodissociation of molecules

The photodissociation of RbI molecules via the second excited state under the action of circularly polarized radiation with a wavelength of 266 nm is studied. By using sub-Doppler Faraday spectroscopy, the angular distributions of the orientation of spins of Rb(5²S_1/2) atoms formed are studied and the anisotropy parameters describing these angular distributions are determined. Based on the anisotropy parameters, the ratio between the amplitudes of the inelastic scattering matrix elements corresponding to the two possible photodissociation channels is determined to be r_Ω=1/r_Ω=0=0.71±0.15, while the phase difference for these matrix elements is found to amount to Δφ = 173° ± 29°.     

Step-step correlations in restricted and self-avoiding random walks

Static step-step correlations for restricted and self-avoiding random walks (SARW) on quadratic and simple cubic lattices are studied with the help of Monte Carlo simulation technique. For the SARW ofN steps our results, for largeN tend to the theoretically predicted values. An analysis of the correlations for SARW in terms of the individual restrictions indicate that its value between steps at a distancer have a dominant contribution coming from the restriction prohibiting polygon closures of sides2r (r2). Our results also show that the contribution of successive restrictions to the mean-square end-to-end distance of a SARW decay with the same exponent as that of the correlations for the SARW.     

Quantum Entanglement and Correlation Lengths of a S-wave Superconductors in the Presence of a Weak Constant External Potential

By considering a s-wave Bardeen-Cooper-Schrieffer superconductor, as a many body system, subject to a weak constant external potential, U, using perturbed linearized Gorkov equations at zero temperature and calculating perturbed Green’s functions up to the first approximation, we obtain the two-particle space-spin density matrix of the system. Then, we investigate the effect of the potential on bipartite entanglement (via concurrence) of electron spins of a Cooper pair and also quantum discord in terms of the potential and the relative distance of electrons of a Cooper pair, r. At some fixed values of r, concurrence is zero and does not change until U increases and receives to a special value. Specially, quantum entanglement length and quantum correlation length (in which quantum discord becomes zero) with respect to the potential are derived. We result that by increasing the potential, these lengths are increased. At higher values of U, quantum correlation length is not very sensitive to changes in U. Finally, the relation between these lengths is given.     

Quantum phase transition in spin-3/2 systems on the hexagonal lattice — optimum ground state approach

Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a one-parametric set of ground states for a five-dimensional manifold of S = 3/2 Hamiltonians. Correlation functions within these ground states are calculated using Monte-Carlo simulations. In contrast to the one-dimensional situation, these states exhibit a parameter-induced second order phase transition. In the disordered phase, two-spin correlations decay exponentially, but in the Néel ordered phase alternating long-range correlations are dominant. We also show that ground state properties can be obtained from the exact solution of a corresponding free-fermion model for most values of the parameter.     

Entanglement in a quantum mixed-spin chain

The pairwise entanglement between neighboring spins in a general mixed-spin chain with arbitrary spins S and 1/2 is investigated in the thermodynamical limit. The entanglement is witnessed by the magnetic susceptibility which determines a characteristic temperature for an entangled thermal state. The characteristic temperature is nearly proportional to the interaction J and the mixed-spin S. The bound of negativity is obtained on the basis of the magnetic susceptibility. It is found that the macroscopic magnetic properties are affected by the quantum entanglement in the real solids.     

Multispin coherences and asymptotic similarity of time correlation functions in solids

The time evolution of multispin (n-particle) correlations in solids (the growth in the number of correlated states) observed by means of multiquantum NMR spectroscopy has been investigated. The contributions from the spins of the immediate environment of each of the spins in the lattice to the time correlation functions that describe this evolution are shown to be mutually asymptotically similar. In this case, the infinite system of coupled ordinary differential equations for the time correlation functions turns out to be equivalent to a diffusion-type partial differential equation with a purely imaginary diffusion coefficient. Its analytical solution has been obtained. It is concluded that the evolution of multispin correlations is probably attributable to multiparticle processes among the spins of a “distant” (with respect to some spin) environment similar to the processes that shape the NMR absorption line wings.     

Theoretical predictions about ENDOR of biradicals in liquid solution

Starting from the equation of motion for the density matrix, ENDOR spectra are computed for a biradical for the first time. The model biradical carries two electronic spins S = 1/2 and two nuclear spins I = 1/2. The relaxation operator is calculated ab initio for three distinct relaxation mechanisms. These mechanisms are the modulation of the isotropic exchange interaction, the hyperfine tensor and the zero-field splitting tensor. The dependence of the ENDOR effect on the amplitudes of the radiofrequency and microwave fields, on the strength of the zero-field splitting tensor, and on the correlation times of the correlation functions is investigated.     

Dilution effect on the compensation temperature in a honeycomb nano-lattice: Monte Carlo study

In this work, we use Monte Carlo simulations with the Metropolis algorithm to study the dilution effect on the magnetic properties in a honeycomb nano-lattice. The geometry of the system is formed by two sub-lattices of 45+45 = 90 atoms consisting of the spins σ = 3/2 and S = 5/2. The ground state phase diagrams at zero absolute temperature are presented. Also, the variation of the total magnetization with reduced temperature for several values of the reduced exchange coupling are discussed. It is found that the compensation temperature depends on the reduced exchange coupling parameters. Furthermore, the dilution of the S spins affects the compensation temperature and hysteresis loops of the studied system.