Spin-spin correlations between two Kondo impurities coupled to an open Hubbard chain

In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we re-examine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling J, the Hubbard interaction U, and the distance R between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior cannot be extracted from these finite-size systems with open boundary conditions.Comment: 8 pages, 10 figures; v2: final version, references and Fig. 8 adde

Finite-Temperature Dynamics and Thermal Intraband Magnon Scattering in Haldane Spin-One Chains

The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations and quantum Monte Carlo simulations. Open finite chains exhibit a sub-gap band in the thermal spectral functions, indicative of localized edge-states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the Haldane spin-one chain is shown to result from intra-band magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio. These findings are discussed with respect to possible future studies on spin-one chain compounds based on inelastic neutron scattering.Comment: 10 pages with 11 figures total (including Supplemental Material); changes in v2: new Figs. S1 and S5, Fig. S3 expanded + related discussion + many smaller modifications to match published versio

Dynamical properties of the sine-Gordon quantum spin magnet Cu-PM at zero and finite temperature

The material copper pyrimidine dinitrate (Cu-PM) is a quasi-one-dimensional spin system described by the spin-1/2 XXZ Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. Based on numerical results obtained by the density-matrix renormalization group, exact diagonalization, and accompanying electron spin resonance (ESR) experiments we revisit the spin dynamics of this compound in an applied magnetic field. Our calculations for momentum and frequency-resolved dynamical quantities give direct access to the intensity of the elementary excitations at both zero and finite temperature. This allows us to study the system beyond the low-energy description by the quantum sine-Gordon model. We find a deviation from the Lorentz invariant dispersion for the single-soliton resonance. Furthermore, our calculations only confirm the presence of the strongest boundary bound state previously derived from a boundary sine-Gordon field theory, while composite boundary-bulk excitations have too low intensities to be observable. Upon increasing the temperature, we find a temperature-induced crossover of the soliton and the emergence of new features, such as interbreather transitions. The latter observation is confirmed by our ESR experiments on Cu-PM over a wide range of the applied field.Comment: 17 pages, 16 figures; published version (including final revisions

Mechanische und spektroskopische Eigenschaften von seltenerd-dotierten Aluminosilicatgläsern

Die dargelegte Arbeit zeigt das hohe Potenzial von seltenerd-dotierten Aluminosilicatgläsern für Lumineszenzanwendungen, die hohe Ansprüche an die mechanische Stabilität fordern. Aufgrund der Vielfalt erzielbarer Materialeigenschaften in Abhängigkeit von der Zusammensetzung, Struktur und Herstellung bietet dieses Glassystem Forschungsansätze für die anwendungsorientierte Entwicklung. In dieser Arbeit wurden Reihen von Glaszusammensetzungen mit spektroskopischen sowie mechanischen Methoden untersucht und Korrelationen zwischen Struktur, Herstellung und Eigenschaften diskutiert. Mit Hilfe der ermittelten Wechselbeziehungen konnten schließlich die Eigenschaften für unterschiedliche Anwendungen systematisch optimiert werden

A Framework for Searching in Graphs in the Presence of Errors

We consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide algorithms for the error-less case and for the independent noise model (where each query independently receives an erroneous answer with known probability p<1/2 and a correct one with probability 1-p). We study this problem both with adversarial errors and independent noise models. First, we show an algorithm that needs at most (log_2 n)/(1 - H(r)) queries in case of adversarial errors, where the adversary is bounded with its rate of errors by a known constant r<1/2. Our algorithm is in fact a simplification of previous work, and our refinement lies in invoking an amortization argument. We then show that our algorithm coupled with a Chernoff bound argument leads to a simpler algorithm for the independent noise model and has a query complexity that is both simpler and asymptotically better than the one of Emamjomeh-Zadeh et al. [STOC 2016]. Our approach has a wide range of applications. First, it improves and simplifies the Robust Interactive Learning framework proposed by Emamjomeh-Zadeh and Kempe [NIPS 2017]. Secondly, performing analogous analysis for edge-queries (where a query to an edge e returns its endpoint that is closer to the target) we actually recover (as a special case) a noisy binary search algorithm that is asymptotically optimal, matching the complexity of Feige et al. [SIAM J. Comput. 1994]. Thirdly, we improve and simplify upon an algorithm for searching of unbounded domains due to Aslam and Dhagat [STOC 1991]

Dynamical properties of the sine Gordon quantum spin magnet Cu PM at zero and finite temperature

The material copper pyrimidine dinitrate Cu PM is a quasi one dimensional spin system described by the spin 1 2 XXZ Heisenberg antiferromagnet with Dzyaloshinskii Moriya interactions. Based on numerical results obtained by the density matrix renormalization group, exact diagonalization, and accompanying electron spin resonance ESR experiments we revisit the spin dynamics of this compound in an applied magnetic field. Our calculations for momentum and frequency resolved dynamical quantities give direct access to the intensity of the elementary excitations at both zero and finite temperature. This allows us to study the system beyond the low energy description by the quantum sine Gordon model. We find a deviation from the Lorentz invariant dispersion for the single soliton resonance. Furthermore, our calculations only confirm the presence of the strongest boundary bound state previously derived from a boundary sine Gordon field theory, while composite boundary bulk excitations have too low intensities to be observable. Upon increasing the temperature, we find a temperature induced crossover of the soliton and the emergence of new features, such as interbreather transitions. The latter observation is confirmed by our ESR experiments on Cu PM over a wide range of the applied fiel