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The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. The impurities effectively cut the chains into finite…
The low energy magnetic excitation spectrum of the Heisenberg antiferromagnetic $S = 1/2$ chain system Sr$_2$CuO$_3$ with Ni- and Ca-impurities is studied by neutron spectroscopy. In all cases, a defect-induced spectral pseudogap is…
The role of inhomegeneity in determining the properties of correlated electron systems is poorly understood because of the dearth of structural probes of disorder at the nanoscale. Advances in both neutron and x-ray scattering…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…
We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods.…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
The exchange interaction between electrons located at different randomly distributed impurities is studied for small density of impurities. The singlet-triplet splitting 2J(R) is calculated for two Coulomb centers at a distance R.…
Low-lying excited states as well as the ground state of the spin-1 antiferromagnetic Heisenberg chain with a spin-1/2 impurity are studied by means of a method of numerical diagonalization. The isotropic nearest-neighbor exchange coupling…
Using numerical Real Space Renormalisation Group methods as well as Stochastic Series Expansions Quantum Monte Carlo simulations a generic model of diluted spin-1/2 impurities interacting at long distances is investigated. Such a model…
We investigate the physics of a magnetic impurity with spin 1/2 in a correlated metallic host. Describing the band by a Hubbard Hamiltonian, the problem is analyzed using dynamical mean-field-theory in combination with Wilson's…
We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from…
The study of randomness in low-dimensional quantum antiferromagnets is at the forefront of research in the field of strongly correlated electron systems, yet there have been relatively few experimental model systems. Complementary neutron…
The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to…
The space- and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behaviour. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in…
The effects of spin-1 impurities introduced in dimerized antiferromagnetic spin chains are studied using Lanczos diagonalization and quantum Monte Carlo simulations. Firstly, the magnitude of the interaction between a Ni-ion replacing a…
We theoretically address the impact of a random distribution of non-magnetic impurities on the surface states formed at the interface between a trivial and a topological insulator. The interaction of electrons with the impurities is…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
Low-lying excited states as well as the ground state of the spin-1 antiferro- magnetic Heisenberg chain with a spin-1/2 impurity are investigated by means of a variational method and a method of numerical diagonalization. It is shown that…