Moment screening in the correlated Kondo lattice model

The magnetic correlations, local moments and the susceptibility in the correlated 2D Kondo lattice model at half filling are investigated. We calculate their systematic dependence on the control parameters J_K/t and U/t. An unbiased and reliable exact diagonalization (ED) approach for ground state properties as well as the finite temperature Lanczos method (FTLM) for specific heat and the uniform susceptibility are employed for small tiles on the square lattice. They lead to two major results: Firstly we show that the screened local moment exhibits non-monotonic behavior as a function of U for weak Kondo coupling J_K. Secondly the temperature dependence of the susceptibility obtained from FTLM allows to extract the dependence of the characteristic Kondo temperature scale T* on the correlation strength U. A monotonic increase of T* for small U is found resolving the ambiguity from earlier investigations. In the large U limit the model is equivalent to the 2D Kondo necklace model with two types of localized spins. In this limit the numerical results can be compared to those of the analytical bond operator method in mean field treatment and excellent agreement for the total paramagnetic moment is found, supporting the reliability of both methods.Comment: 19 pages, 9 figure

Similar temperature scale for valence changes in Kondo lattices with different Kondo temperatures

The Kondo model predicts that both the valence at low temperatures and its temperature dependence scale with the characteristic energy T_K of the Kondo interaction. Here, we study the evolution of the 4f occupancy with temperature in a series of Yb Kondo lattices using resonant X-ray emission spectroscopy. In agreement with simple theoretical models, we observe a scaling between the valence at low temperature and T_K obtained from thermodynamic measurements. In contrast, the temperature scale T_v at which the valence increases with temperature is almost the same in all investigated materials while the Kondo temperatures differ by almost four orders of magnitude. This observation is in remarkable contradiction to both naive expectation and precise theoretical predictions of the Kondo model, asking for further theoretical work in order to explain our findings. Our data exclude the presence of a quantum critical valence transition in YbRh2Si2

Multiple-charge transfer and trapping in DNA dimers

We investigate the charge transfer characteristics of one and two excess charges in a DNA base-pair dimer using a model Hamiltonian approach. The electron part comprises diagonal and off-diagonal Coulomb matrix elements such a correlated hopping and the bond-bond interaction, which were recently calculated by Starikov [E. B. Starikov, Phil. Mag. Lett. {\bf 83}, 699 (2003)] for different DNA dimers. The electronic degrees of freedom are coupled to an ohmic or a super-ohmic bath serving as dissipative environment. We employ the numerical renormalization group method in the nuclear tunneling regime and compare the results to Marcus theory for the thermal activation regime. For realistic parameters, the rate that at least one charge is transferred from the donor to the acceptor in the subspace of two excess electrons significantly exceeds the rate in the single charge sector. Moreover, the dynamics is strongly influenced by the Coulomb matrix elements. We find sequential and pair transfer as well as a regime where both charges remain self-trapped. The transfer rate reaches its maximum when the difference of the on-site and inter-site Coulomb matrix element is equal to the reorganization energy which is the case in a GC-GC dimer. Charge transfer is completely suppressed for two excess electrons in AT-AT in an ohmic bath and replaced by damped coherent electron-pair oscillations in a super-ohmic bath. A finite bond-bond interaction $W$ alters the transfer rate: it increases as function of $W$ when the effective Coulomb repulsion exceeds the reorganization energy (inverted regime) and decreases for smaller Coulomb repulsion

Exact Constructions in the (Non-linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers

In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of Conti et al. (Proc R Soc A 73(2203):20170235, 2017). Passing to the limit $n\rightarrow\infty$, this allows us to treat solid crystals and nematic elastomer differential inclusions simultaneously. In particular, we recover and generalise (non-linear) planar tripole star type deformations which were experimentally observed in Kitano and Kifune (Ultramicroscopy 39(1–4):279–286, 1991), Manolikas and Amelinckx (Physica Status Solidi (A) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980). Furthermore, we discuss the corresponding geometrically linearised problem

Kondo Effect in a Metal with Correlated Conduction Electrons: Diagrammatic Approach

We study the low-temperature behavior of a magnetic impurity which is weakly coupled to correlated conduction electrons. To account for conduction electron interactions a diagrammatic approach in the frame of the 1/N expansion is developed. The method allows us to study various consequences of the conduction electron correlations for the ground state and the low-energy excitations. We analyse the characteristic energy scale in the limit of weak conduction electron interactions. Results are reported for static properties (impurity valence, charge susceptibility, magnetic susceptibility, and specific heat) in the low-temperature limit.Comment: 16 pages, 9 figure

Modification of the standard model for the lanthanides

We show that incorporation of strong electron correlations into the Kohn-Sham scheme of band structure calculations leads to a modification of the standard model of the lanthanides and that this procedure removes the existing discrepancy between theory and experiment concerning the ground state properties. Within the picture suggested, part of the upper Hubbard $f$-band is occupied due to conduction band-$f$-mixing interaction (that is renormalized due to correlations) and this contributes to the cohesive energy of the crystal. The lower Hubbard band has zero width and describes fermionic excitations in the shell of localized $f$-s. Fully self-consistent calculations (with respect to both charge density and many-electron population numbers of the $f$-shell) of the equilibrium volume $V_0$ and the bulk modulus of selected lanthanides have been performed and a good agreement is obtained.Comment: 1 fi

Quasiparticle Interactions for f2^2-Impurity Anderson Model with Crystalline-Electric-Field: Numerical Renormalization Group Study

The aspect of the quasiparticle interaction of a local Fermi liquid, the impurity version of f$^2$-based heavy fermions, is studied by the Wilson numerical renormalization group method. In particular, the case of the f$^2$-singlet crystalline-electric-field ground state is investigated assuming the case of UPt$_3$ with the hexagonal symmetry. It is found that the interorbital interaction becomes larger than the intraorbital one in contrast to the case of the bare Coulomb interaction for the parameters relevant to UPt$_3$. This result offers us a basis to construct a microscopic theory of the superconductivity of UPt$_3$ where the interorbital interactions are expected to play important roles.Comment: 9 pages, 5 figure

Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea