Matrix product state formulation of frequency-space dynamics at finite temperatures

We present a flexible density-matrix renormalization group approach to calculate finite-temperature spectral functions of one-dimensional strongly correlated quantum systems. The method combines the purification of the finite-temperature density operator with a moment expansion of the Green's function. Using this approach, we study finite-temperature properties of dynamical spectral functions of spin-1/2 XXZ chains with Dzyaloshinskii-Moriya interactions in magnetic fields and analyze the effect of these symmetry breaking interactions on the nature of the finite-temperature dynamic spin structure factor.Comment: 5 pages (3 figures) + 2 pages supplemental material; v3: final versio

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

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

Magnetic excitations in the S = 1/2 antiferromagnetic-ferromagnetic chain compound BaCu2V2O8 at zero and finite temperature

Unlike most quantum systems which rapidly become incoherent as temperature is raised, strong correlations persist at elevated temperatures in $S=1/2$ dimer magnets, as revealed by the unusual asymmetric lineshape of their excitations at finite temperatures. Here we quantitatively explore and parameterize the strongly correlated magnetic excitations at finite temperatures using the high resolution inelastic neutron scattering on the model compound BaCu$_2$V$_2$O$_8$ which we show to be an alternating antiferromagnetic-ferromagnetic spin$-1/2$ chain. Comparison to state of the art computational techniques shows excellent agreement over a wide temperature range. Our findings hence demonstrate the possibility to quantitatively predict coherent behavior at elevated temperatures in quantum magnets.Comment: 5 pages + 6 pages supplement; problems with list of references are fixe

Computational-Statistical Gaps for Improper Learning in Sparse Linear Regression

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in time polynomial in $d$, $k$, and $n$) find a potentially dense estimate for the regression vector that achieves non-trivial prediction error on the $n$ samples. Information-theoretically this can be achieved using $\Theta(k \log (d/k))$ samples. Yet, despite its prominence in the literature, there is no polynomial-time algorithm known to achieve the same guarantees using less than $\Theta(d)$ samples without additional restrictions on the model. Similarly, existing hardness results are either restricted to the proper setting, in which the estimate must be sparse as well, or only apply to specific algorithms. We give evidence that efficient algorithms for this task require at least (roughly) $\Omega(k^2)$ samples. In particular, we show that an improper learning algorithm for sparse linear regression can be used to solve sparse PCA problems (with a negative spike) in their Wishart form, in regimes in which efficient algorithms are widely believed to require at least $\Omega(k^2)$ samples. We complement our reduction with low-degree and statistical query lower bounds for the sparse PCA problems from which we reduce. Our hardness results apply to the (correlated) random design setting in which the covariates are drawn i.i.d. from a mean-zero Gaussian distribution with unknown covariance.Comment: 24 pages; updated typos, some explanations, and reference

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