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The ferroelectric to paraelectric phase transition in LiTaO$_3$ and in pure as well as Mg doped LiNbO$_3$ is investigated theoretically by atomistic calculations in the framework of the density functional theory, as well as experimentally by calorimetry and electrical conductivity measurements. First principles models within the stochastic self-consistent harmonic approximation (SSCHA) allow to consider anharmonic effects and thus to obtain a realistic estimate of the Curie temperature $T_C$ of both ferroelectrics. \textit{Ab initio} molecular dynamics (AIMD) calculations performed on large supercells confirm the Curie temperatures estimated with the SSCHA approach. Moreover, they also suggest that the structural phase transition is a continuous process beginning at temperatures well below $T_C$. According to AIMD, significant ionic displacements occurr already at temperatures of about 100\,K and 300\,K below $T_C$ in LiTaO$_3$ and LiNbO$_3$, respectively. To asses whether and how far the ionic displacements affect the materials properties, the AIMD results are compared with measurements of the electrical conductivity and of the heat capacity across the phase transition. Our first principles calculations moreover show that Mg ions, a frequently employed dopant, raise the Curie temperature in LiNbO$_3$.

The investigation of the structural phase transition in the vicinity of the Curie temperature $T_c$ of LiNb$_{1-x}$Ta$_x$O$_3$ crystals is motivated by the expected combination of advantageous high-temperature properties of LiNbO$_3$ and LiTaO$_3$, including high piezoelectric modules and remarkable high-temperature stability, respectively. $T_c$ marks the ultimate limit for exploiting the piezoelectric properties, however transition related structural modifications might impact this and other properties even below $T_c$. Remarkably, the phase transition from the ferroelectric to the paraelectric phase, whose temperature strongly depends on the composition $x$, shows a significant drop in the activation energy of the electrical conductivity. The magnitude, temperature dependence and underlying mechanisms of this drop are discussed from a microscopic perspective. Molecular dynamics calculations in the framework of the density functional theory show that substantial displacements of the cations occur below $T_c$ for both the end compounds LiNbO$_3$ and LiTaO$_3$, and might thus affect the electrical conductivity. Above $T_c$, the migration of lithium ions is presumably facilitated by a shortened diffusion path for the most favorable jump of the lithium ions. Electronic contributions to the conductivity, which become important above 900 K, are explained within the polaronic picture by the formation and migration of free small polarons., Comment: I submitted it to The Physica Status Solidi A: Applications and Materials Science on 12/21/2023 and it's under review. It will be updated after receiving reviews

Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians represent an important direction in the field. Among these techniques the method, presented here, might be that approach with the widest range of possible applications: We demonstrate that both stepwise and continuous unitary transformations to diagonalize the many-particle Hamiltonian as well as perturbation theory and also non-perturbative treatments can be understood within the same theoretical framework. The new method is based on the introduction of generalized projection operators and allows to develop a renormalization scheme which is used to evaluate directly the physical quantities of a many-particle system. The applicability of this approach is shown for two important elementary many-particle problems., Comment: 19 pages, 6 figures

We present an extended version of the projector-based renormalization method that can be used to address not only equilibrium but also non-equilibrium situations in coupled fermion-boson systems. The theory is applied to interacting electrons, holes and photons in a semiconductor microcavity, where the loss of cavity photons into vacuum is of particular importance. The method incorporates correlation and fluctuation processes beyond mean-field theory in a wide parameter range of detuning, Coulomb interaction, light-matter coupling and damping, even in the case when the number of quasiparticle excitations is large. This enables the description of exciton and polariton formation, and their possible condensation through spontaneous phase symmetry breaking by analyzing the ground-state, steady-state and spectral properties of a rather generic electron-hole-photon Hamiltonian, which also includes the coupling to two fermionic baths and a free-space photon reservoir. Thereby, the steady-state behavior of the system is obtained by evaluating expectation values in the long-time limit by means of the Mori-Zwanzig projection technique. Tracking and tracing different order parameters, the fully renormalized single-particle spectra and the steady-state luminescence, we demonstrate the Bose-Einstein condensation of excitons and polaritons and its smooth transition when the excitation density is increased., Comment: revised version, 30 pages, 9 figures

We study the competition between unconventional superconducting pairing and charge density wave (CDW) formation for the two-dimensional Edwards Hamiltonian at half filling, a very general two-dimensional transport model in which fermionic charge carriers couple to a correlated background medium. Using the projective renormalization method we find that a strong renormalization of the original fermionic band causes a new hole-like Fermi surface to emerge near the center of the Brillouin zone, before it eventually gives rise to the formation of a charge density wave. On the new, disconnected parts of the Fermi surface superconductivity is induced with a sign-changing order parameter. We discuss these findings in the light of recent experiments on iron-based oxypnictide superconductors., Comment: 13 pages, 2 figures

We propose a projector-based renormalization framework to study exciton-polariton Bose-Einstein condensation in a microcavity matter-light system. Treating Coulomb interaction and electron-hole/photon coupling effects on an equal footing we analyze the ground-state properties of the exciton polariton model according to the detuning and the excitation density. We demonstrate that the condensate by its nature shows a crossover from an excitonic insulator (of Bose-Einstein respectively BCS type) to a polariton and finally photonic condensed state as the excitation density increases at large detuning. If the detuning is weak polariton or photonic phases dominate. While in both cases a notable renormalization of the quasiparticle band structure occurs that strongly affects the coherent part of the excitonic luminescence, the incoherent wavevector-resolved luminescence spectrum develops a flat bottom only for small detuning., Comment: 18 pages, 17 figures, final version

In domains like automotive, safety-critical features are increasingly realized by software. Some features might even require fail-operational behavior, so that they must be provided even in the presence of random hardware failures. A new fault-tolerant SW/HW architecture for electric vehicles provides inherent safety capabilities that enable fail-operational features. In this paper we introduce a formal model of this architecture and an approach to calculate valid deployments of mixed-critical software-components to the execution nodes, while ensuring fail-operational behavior of certain components. Calculated redeployments cover the cases in which faulty execution nodes have to be isolated. This allows to formally analyze which set of features can be provided under decreasing available execution resources., Comment: EDCC-2014, EDSoS-2014, Fault-Tolerance, Fail-Operational, Deployment

The explicit evaluation of linear response coefficients for interacting many-particle systems still poses a considerable challenge to theoreticians. In this work we use a novel many-particle renormalization technique, the so-called projector-based renormalization method, to show how such coefficients can systematically be evaluated. To demonstrate the prospects and power of our approach we consider the dynamical wave-vector dependent spin susceptibility of the two-dimensional Hubbard model and also determine the subsequent magnetic phase diagram close to half-filling. We show that the superior treatment of (Coulomb) correlation and fluctuation effects within the projector-based renormalization method significantly improves the standard random phase approximation results., Comment: 17 pages, 7 figures, revised version

Using the projector-based renormalization method we investigate the formation of the excitonic insulator phase in the two-dimensional (2D) spinless Falicov-Kimball model with dispersive $f$ electrons and address the existence of excitonic bound states at high temperatures on the semiconductor side of the semimetal-semiconductor transition. To this end we calculate the imaginary part of the dynamical electron-hole pair susceptibility and analyze the wave-vector and energy dependence of excitonic resonances emerging in the band gap. We thereby confirm the existence of the exciton insulator and its exciton environment within a generic two-band lattice model with local Coulomb attraction., Comment: 6 pages, 5 figures, final version

We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral functions. Our numerical results proved the valence transition picture, related to the appearance of the excitonic insulator phase, in the case of overlapping $c$ and $f$ bands. Thereby the photoemission spectra show significant differences between the weak-to-intermediate and intermediate-to-strong Coulomb attraction regimes, indicating a BCS-BEC transition of the excitonic condensate., Comment: final version, minor corrections in the text, references updated

We discuss the magnetic properties of a dimerized and completely frustrated tetrahedral spin-1/2 chain. Using a combination of exact diagonalization and bond-operator theory the quantum phase diagram is shown to incorporate a singlet-product, a dimer, and a Haldane phase. In addition we consider one-, and two-triplet excitations in the dimer phase and evaluate the magnetic Raman cross section which is found to be strongly renormalized by the presence of a two-triplet bound state. The link to a novel tellurate materials is clarified., Comment: 8 pages, 8 figures

The two-layer square lattice quantum antiferromagnet with spins 1/2 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram., Comment: 12 pages, 9 figs; added references; final version as published

Magnetic properties of a completely frustrated tetrahedral chain are briefly summarized. Using exact diagonalization, and bond-operator theory results for the ground-state phase diagram, the one-triplet excitations and the Raman spectrum are given. The link to novel tellurate materials is clarified., Comment: 2 pages, 3 figures

Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other treatments. As a nontrivial example of use the derived method is applied to the strong-coupling limit of the half-filled Hubbard model on a general lattice in arbitrary spatial dimension for which the fourth-order expansion in t/U of the effective Hamiltonian is derived., Comment: 9 pages, 5 figures included; accepted for publication in J. Phys.: Condens. Matter

The two-layer square lattice quantum antiferromagnet with spins 1/2 shows a magnetic order-disorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a t-J Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system which covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics of both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at (pi/2,pi/2). For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The cross-over between these two scenarios occurs inside the antiferromagnetic phase which indicates that the hole dynamics is governed by the local environment of the hole., Comment: 14 pages, 11 figs, minor changes, discussion of spin correlations added, accepted for publication in PRB

We study frequency- and wave-vector dependent charge correlations in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t-J model. The ground state is expressed within a cumulant formalism which has been successfully applied to study magnetic properties of the weakly doped system. Within this approach the ground state contains independent spin-bag quasiparticles (magnetic polarons). We present results for the charge-density response function and for the optical conductivity at zero temperature for different values of t/J. They agree well with numerical results calculated by exact diagonalization techniques. The density response function for intermediate and large momenta shows a broad continuum on energy scales of order of several t whereas the optical conductivity for \omega > 0 is dominated by low energy excitations (at 1.5 - 2 J). We show that these weak-doping properties can be well understood by transitions between excited states of spin-bag quasiparticles., Comment: 10 pages, 5 figs., to appear in Europ. Phys. J. B

The motion of a single hole in an arbitrary magnetic background is investigated for the 2D t-J model. The wavefunction of the hole is described within a generalized string picture which leads to a modified concept of spin polarons. We calculate the one-hole spectral function using a large string basis for the limits of a Neel ordered and a completely disordered background. In addition we use a simple approximation to interpolate between these cases. For the antiferromagnetic background we reproduce the well-known quasiparticle band. In the disordered case the shape of the spectral function is found to be strongly momentum-dependent, the quasiparticle weight vanishes for all hole momenta. Finally, we discuss the relevance of results for the lowest energy eigenvalue and its dispersion obtained from calculations using a polaron of minimal size as found in the literature., Comment: 13 pages, 8 figures, to appear in Phys. Rev. B

Current methods to describe the thermodynamic behavior of many-particle systems are often based on perturbation theory with an unperturbed system consisting of free particles. Therefore, only a few methods are able to describe both strongly and weakly correlated systems along the same lines. In this article we propose a cumulant approach which allows for the evaluation of excitation energies and is especially appropriate to account for the thermodynamics at low temperatures. The method is an extension of a cumulant formalism which was recently proposed to study statical and dynamical properties of many-body systems at zero temperature. The present approach merges into the former one for vanishing temperature. As an application we investigate the thermodynamics of the hole-doped antiferromagnetic phase in high-temperature superconductors in the framework of the anisotropic t-J model., Comment: 17 pages, 3 figures, to appear in Phys. Rev. B

We investigate the dynamical charge-charge correlation function and the optical conductivity in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t-J model. The arising matrix elements are evaluated within a cumulant formalism which was recently applied to investigate magnetic properties of weakly doped antiferromagnets. Within the present approach the ground state consists of non-interacting hole quasiparticles. Our spectra agree well with numerical results calculated via exact diagonalization techniques. The method we employ enables us to explain the features present in the correlation functions. We conclude that the charge dynamics at weak doping is governed by transitions between excited states of spin-bag quasiparticles., Comment: 5 pages, 2 figures, to appear in Europhys. Letters

We present a new approach to static and dynamical properties of holes and spins in weakly doped antiferromagnets in two dimensions. The calculations are based on a recently introduced cumulant approach to ground--state properties of correlated electronic systems. The present method allows to evaluate hole and spin--wave dispersion relations by considering hole or spin excitations of the ground state. Usually, these dispersions are found from time--dependent correlation functions. To demonstrate the ability of the approach we first derive the dispersion relation for the lowest single hole excitation at half--filling. However, the main purpose of this paper is to focus on the mutual influence of mobile holes and spin waves in the weakly doped system. It is shown that low-energy spin excitations strongly admix to the ground--state. The coupling of spin waves and holes leads to a strong suppression of the staggered magnetization which can not be explained by a simple rigid--band picture for the hole quasiparticles. Also the experimentally observed doping dependence of the spin--wave excitation energies can be understood within our formalism., Comment: REVTEX, 25 pages, 7 figures (EPS), to be published in Phys. Rev. B