We investigate static correlation and delocalization errors in the self-consistent $GW$ and random-phase approximation (RPA) by studying molecular dissociation of the ${\mathrm{H}}_2$ and LiH molecules. Although both approximations contain topologically identical diagrams, the nonlocality and frequency dependence of the $GW$ self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies, which allow for a better description of static correlation at intermediate bond distances. The substantial error found in $GW$ is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation, their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in $GW$ making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulas for the $GW$ Green's function and total energy of a simplified two-level model providing additional insights into the dissociation limit.

The magnetic anisotropy of $\mathrm{TbMn}{\mathrm{O}}_3$ was explored by means of polarized x-ray absorption spectroscopy and x-ray magnetic circular dichroism (XMCD) measurements at the $\mathrm{Mn}{L}_{2,3}$ and $\mathrm{Tb}{M}_{4,5}$ edges as a function of temperature and magnetic-field intensity. The selective magnetometry measurements were compared with the macroscopic magnetic properties on single crystals. XMCD measurements at the $\mathrm{Tb}{M}_{4,5}$ edge as a function of the magnetic field reproduces quite well the macroscopic magnetic anisotropy at low temperatures with the Tb moments staying confined along their Ising axis within the $ab$ plane, whereas a weak XMCD signal is observed at the $\mathrm{Mn}{L}_{2,3}$ edge. These results point out that $\mathrm{T}{\mathrm{b}}^{3+}$ single-ion anisotropy is the only responsible for the magnetic anisotropy on this multiferroic compound at high magnetic fields. Moreover, we found $\mathrm{Mn}{L}_{2,3}$ XMCD measurements show that the cycloidal antiferromagnetic order is almost unaffected by the applied magnetic field at low temperatures under an applied magnetic field. Therefore, we discuss that this strong Ising nature of $\mathrm{T}{\mathrm{b}}^{3+}$ ions, through a magnetocrystalline coupling mediated by the oxygen atoms, must play an important role in the field-induced electric polarization flop and therefore in the magnetoelectric coupling on $\mathrm{TbMn}{\mathrm{O}}_3$.

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting, one-dimensional systems, such as Coulombic and dipolar systems, and quasi-two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.

Starting from general total-energy considerations, we demonstrate that the SU(2) spin-rotation symmetry and the resulting persistent helical state (PHS) predicted to occur in an electron system with equal Rashba-Dresselhaus coupling constants are not in fact realized. On account of the accidental degeneracy that appears in the single-particle spectrum, the Coulomb interaction favors the apparition of an itinerant antiferromagnetic (IAF) order characterized by a fractional polarization of fixed spatial orientation. Within the Hartree-Fock approximation, we obtain numerical results that describe the temperature evolution of the order parameter in the IAF state and determine the critical temperature of the transition to the paramagnetic state.

We use ab initio simulations to study the static and dynamic properties of a sodium borosilicate liquid with composition $3{\mathrm{Na}}_2\mathrm{O}–{\mathrm{B}}_2{\mathrm{O}}_3–6{\mathrm{SiO}}_2$, i.e., a system that is the basis of many glass-forming materials. In particular, we focus on the question how boron is embedded into the local structure of the silicate network liquid. From the partial structure factors we conclude that there is a weak nanoscale phase separation between silicon and boron and that the sodium atoms form channel-like structures as they have been found in previous studies of sodosilicate glass-formers. Our results for the x-ray and neutron structure factor show that this feature is basically not detectable in the former but should be visible in the latter as a small peak at small wave vectors. At high temperatures we find a high concentration of threefold coordinated boron atoms which decreases rapidly with decreasing $T$, whereas the number of fourfold coordinated boron atoms increases. Therefore, we conclude that at the experimental glass transition temperature most boron atoms will be fourfold coordinated. We show that the transformation of ${}^{\left[3\right]}\mathrm{B}$ into ${}^{\left[4\right]}\mathrm{B}$ with decreasing $T$ is not just related to the diminution of nonbridging oxygen atoms as claimed in previous studies, but to a restructuring of the silicate matrix. The diffusion constants of the various elements show an Arrhenius behavior and we find that the one for boron has the same value as the one of oxygen and is significantly larger than the one of silicon. This shows that these two network-formers have rather different dynamical properties, a result that is also confirmed from the time dependence of the van Hove functions. Finally, we show that the coherent intermediate scattering function for the sodium atoms is very different from the incoherent one and that it tracks the one of the matrix atoms.

We use ab initio simulations to investigate the properties of a sodium borosilicate glass of composition ${3\mathrm{Na}}_2\mathrm{O}-{\mathrm{B}}_2{\mathrm{O}}_3-6{\mathrm{SiO}}_2$. We find that the broadening of the first peak in the radial distribution functions $g_{\mathrm{BO}}\left(r\right)$ and $g_{\mathrm{BNa}}\left(r\right)$ is due to the presence of trigonal and tetrahedral boron units as well as to nonbridging oxygen atoms connected to ${\mathrm{BO}}_3$ units. In agreement with experimental results, we find that the ${}^{\left[3\right]}\mathrm{B}$  units involve a significant number of nonbridging oxygens, whereas the vast majority of ${}^{\left[4\right]}\mathrm{B}$ have only bridging oxygens. We determine the three-dimensional distribution of the Na atoms around the ${}^{\left[3\right]}\mathrm{B}$  and ${}^{\left[4\right]}\mathrm{B}$  units and use this information to explain why the sodium atoms associated with the latter share more oxygen atoms with the central boron atoms than the former units. From the distribution of the electrons we calculate the total electronic density of states, as well its decomposition into angular momentum contributions. The vibrational density of states shows at high frequencies a band that originates from the motion of the boron atoms. We find that the ${}^{\left[3\right]}\mathrm{B}$  and ${}^{\left[4\right]}\mathrm{B}$  units give rise to well-defined features in the spectrum, which thus can be used to estimate the concentration of these structural entities. The contribution of ${}^{\left[3\right]}\mathrm{B}$  can be decomposed further into symmetric and asymmetric parts that can also be easily identified in the spectrum. Furthermore, it is found that certain features in the spectrum can be used to obtain information on the type of atom that is the second-nearest neighbor of a boron in the ${}^{\left[4\right]}\mathrm{B}$  unit. We calculate the average Born charges on the bridging and nonbridging oxygen atoms and show that these depend linearly on the angle between the two bonds and the distance from the connected cation, respectively. Finally, we have determined the frequency dependence of the dielectric function, as well as the absorption spectra. The latter is in good quantitative agreement with the experimental data.

We have investigated the magnetic response of ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3/{\mathrm{SrRuO}}_3$ superlattices to biaxial in-plane strain applied in situ. Superlattices grown on piezoelectric substrates of $0.72{\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3-0.28{\mathrm{PbTiO}}_3\left(001\right)$ (PMN-PT) show strong antiferromagnetic coupling of the two ferromagnetic components. The coupling field of ${\mu }_0{H}_{AF}=1.8$ T is found to change by ${\mu }_0▵H_{AF}/▵\varepsilon \sim -520$ mT %${}^{-1}$ under reversible biaxial strain $▵\varepsilon$ at 80 K in a [${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$($22\text{Å}$)/${\mathrm{SrRuO}}_3$($55\text{Å}$)${\mathrm{]}}_{15}$ superlattice. This reveals a significant strain effect on interfacial coupling. The applied in-plane compression enhances the ferromagnetic order in the manganite layers, which are under as-grown tensile strain, leading to a larger net coupling of ${\mathrm{SrRuO}}_3$ layers at the interface. It is thus difficult to disentangle the contributions from strain-dependent antiferromagnetic Mn-O-Ru interface coupling and Mn-O-Mn ferromagnetic double exchange near the interface for the strength of the apparent antiferromagnetic coupling. We discuss our results in the framework of available models.

Spin-dimer systems are a versatile playground for the detailed study of quantum phase transitions. Using the magnetic field as the tuning parameter, it is possible to observe a crossover from the characteristic scaling near critical points to the behavior of a finite-temperature phase transition. In this work we study two-dimensional coupled spin-dimer systems by comparing numerical quantum Monte Carlo simulations with analytical calculations of the susceptibility, the magnetocaloric effect, and the helicity modulus. The magnetocaloric behavior of the magnetization with temperature can be used to determine the critical fields with high accuracy, but the critical scaling does not show the expected logarithmic corrections. The zeros of the cooling rate are an excellent indicator of the competition between quantum criticality and vortex physics, but they are not directly associated with the quantum phase transition or the finite-temperature Berezinsky-Kosterlitz-Thouless transition. The results give a unified picture of the full quantum and finite-temperature phase diagram.

Synchrotron-radiation-based Mössbauer absorption spectroscopy of ${}^{40}\mathrm{K}$ nuclei was performed. We investigated potassium nanoclusters arrayed in a porous crystal of sodalite. The nanoclusters exhibit antiferromagnetic (AFM) ordering below $\simeq 72$ K. The energy-domain ${}^{40}\mathrm{K}$ Mössbauer spectra were successfully obtained in the temperature range of 8–140 K. Precise analysis of the spectra indicates the appearance of a hyperfine magnetic field at low temperatures. The hyperfine field was evaluated to be $9.2\pm 3.0$ T at 8 K. This result signifies the spontaneous polarization of s-electron spins in three-dimensionally arrayed potassium nanoclusters in AFM-ordered states.

We demonstrate that the tunneling spectra from deeply underdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_{6+\delta }$ (Bi2201) and ${\mathrm{Ca}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ (CCOC) provide clear evidence for a nanoscale phase separation (NPS), which causes the gap to fill rather than close with doping. The phase separation extends from half-filling to a doping of $x\sim 0.09$. Assuming that the NPS is in the form of stripes, the nodal gap, which we model as a Coulomb gap, arises from impurity pinning of the charged stripes, and ultimately drives a metal-insulator transition.

In ferromagnet/heavy-metal bilayers, an in-plane current gives rise to spin-orbit spin-transfer torque, which is usually decomposed into fieldlike and dampinglike torques. For two-dimensional free-electron and tight-binding models with Rashba spin-orbit coupling, the fieldlike torque acquires nontrivial dependence on the magnetization direction when the Rashba spin-orbit coupling becomes comparable to the exchange interaction. This nontrivial angular dependence of the fieldlike torque is related to the Fermi surface distortion, determined by the ratio of the Rashba spin-orbit coupling to the exchange interaction. On the other hand, the dampinglike torque acquires nontrivial angular dependence when the Rashba spin-orbit coupling is comparable to or stronger than the exchange interaction. It is related to the combined effects of the Fermi surface distortion and the Fermi sea contribution. The angular dependence is consistent with experimental observations and can be important to understand magnetization dynamics induced by spin-orbit spin-transfer torques.

Off-stoichiometry, epitaxial $\mathrm{F}{\mathrm{e}}_x\mathrm{S}{\mathrm{i}}_{1-x}$ thin films $(0.5<x<1.0)$ exhibit $D{0}_3$ or $B2$ chemical order, even far from stoichiometry. Theoretical calculations show the magnetic moment is strongly enhanced in the fully chemically disordered $A2$ phase, while both theoretical and experimental results show that the magnetization is nearly the same in the $B2$ and $D{0}_3$ phases, meaning partial chemical disorder does not influence the magnetism. The dependencies of the magnetic moments are directly and nonlinearly linked to the number of Si atoms, primarily nearest neighbor but also to a lesser extent (up to 10%) next nearest neighbor, surrounding Fe, explaining the similarities between $B2$ and $D{0}_3$ and the strong enhancement for the $A2$ structure. The calculated electronic density of states shows many similarities in both structure and spin polarization between the $D{0}_3$ and $B2$ structures, while the $A2$ structure exhibits disorder broadening and a reduced spin polarization.

We have prepared two sets of polycrystalline samples of ${\mathrm{Nd}}_{1-x}{\mathrm{Eu}}_x{\mathrm{CrTiO}}_5$ and ${\mathrm{NdCr}}_{1-y}{\mathrm{Al}}_y{\mathrm{TiO}}_5$, and have measured susceptibility, dielectric constant polarization, and specific heat below 30 K. In both sets, we find that the antiferromagnetic temperature systematically decreases with increasing impurity concentrations. This clearly indicates that not only Cr but also Nd is essential to the magnetic order in the title compound. Such a cooperative behavior of the $4f$ and $3d$ moments is quite unique in comparison with other complex oxides. A possible mechanism of the magnetic order and magnetoelectric response is discussed.

We study the mechanism of the triplet superconductivity (TSC) in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ based on the multiorbital Hubbard model. The electronic states are studied using the recently developed renormalization group method combined with the constrained random-phase approximation, called the RG + cRPA method. Thanks to the vertex correction (VC) for the susceptibility, which is dropped in the mean-field-level approximations, strong orbital and spin fluctuations at $\mathit{Q}\approx (2\pi /3,2\pi /3)$ emerge in the quasi-one-dimensional Fermi surfaces (FSs) composed of $d_{xz}+d_{yz}$ orbitals. Due to the cooperation of both fluctuations, we obtain the triplet superconductivity in the $E_u$ representation, in which the superconducting gap is given by the linear combination of $({\Delta }_x\left(\mathit{k}\right),{\Delta }_y\left(\mathit{k}\right))\sim (sin3k_x,sin3k_y)$. Very similar results are obtained by applying the diagrammatic calculation called the self-consistent VC method. Thus, the idea of “orbital + spin fluctuation mediated TSC” is confirmed by both the RG + cRPA method and the self-consistent VC method. We also revealed that the large superconducting gap on the $d_{xy}$-orbital Fermi surface is induced from gaps on the quasi-one-dimensional FSs, in consequence of the large orbital mixture due to the $4d$ spin-orbit interaction.

High-resolution resonant inelastic x-ray scattering (RIXS) at the oxygen $K$ edge has been used to study the orbital excitations of ${\text{Ca}}_2{\text{RuO}}_4$ and ${\text{Sr}}_2{\text{RuO}}_4$. In combination with linear dichroism x-ray absorption spectroscopy, the ruthenium $4d$-orbital occupation and excitations were probed through their hybridization with the oxygen $p$ orbitals. These results are described within a minimal model, taking into account crystal field splitting and a spin-orbit coupling ${\lambda }_{so}=200$ meV. The effects of spin-orbit interaction on the electronic structure and implications for the Mott and superconducting ground states of (Ca,Sr)${}_2\mathrm{RuO}{}_4$ are discussed.

Chromium-doped hexagonal barium titanate is studied with first-principles density functional theory. The results are compared with experimental data available from electron paramagnetic resonance, x-ray diffraction, and optical absorption spectra. The probable site for the impurity atom occupancy in the lattice, their probable charge states, and the role of oxygen vacancies in their stabilization are investigated. Defect formation energy is used to analyze the role of electronic- and ionic-compensation mechanisms in stabilizing the point defect. Various atomic positions for the oxygen vacancy surrounding the impurity atom are taken into consideration in order to compare with some of the conclusions derived from experiments. Our results on the substitutional site preference and the location of oxygen vacancy in the next-neighbor surrounding of the impurity Cr are in good agreement with experiments.

Exciton Mott transition (EMT) in Ge was investigated by using optical-pump and terahertz-probe spectroscopy. From the quantitative analysis of optical conductivity and dielectric function, we evaluated the densities of unbound electron-hole pairs and excitons after the photoexcitation, from which we determined the ionization ratio of excitons α. The Mott crossover density region in Ge was elucidated from the density dependence of α in the temperature range above the critical temperature of electron-hole droplets. The $1s-2p$ excitonic transition energy hardly shifted with increasing density toward the EMT. Combined with the similar results recently observed in bulk Si, we suggest that the robustness of excitonic correlation against the Coulomb screening is a universal feature in bulk semiconductors in the Mott crossover regime.