Dynamical Mean-field Approach Research Articles

Dynamical mean-field approach to disordered interacting systems and applications to the quantum transport problem

Dynamical mean-field approach to disordered interacting systems and applications to the quantum transport problem

Dynamical mean-field approach to Ising models with impurities

Dynamical mean-field approach to Ising models with impurities

SU(4)-symmetric Hubbard model at quarter filling: Insights from the dynamical mean-field approach

We apply the dynamical mean-field approach to the four-component SU(4)-symmetric Fermi-Hubbard model to study transitions between different magnetically ordered phases as well as the hysteresis behavior in the unordered regime. At quarter filling (one particle per site) on the square lattice we identify both the two-sublattice and plaquette-ordered antiferromagnetic phases with the corresponding entropy-driven hierarchy for critical temperatures. We also analyze the behavior of thermodynamic characteristics: the local double occupancy, compressibility, and entropy per particle, which are relevant for experiments with ultracold alkaline-earth(-like) atoms in optical lattices.

Driven dynamics of a quantum dot electron spin coupled to a bath of higher-spin nuclei

The interplay of optical driving and hyperfine interaction between an electron confined in a quantum dot and its surrounding nuclear spin environment produces a range of interesting physics such as mode-locking. In this work, we go beyond the ubiquitous spin 1/2 approximation for nuclear spins and present a comprehensive theoretical framework for an optically driven electron spin in a self-assembled quantum dot coupled to a nuclear spin bath of arbitrary spin. Using a dynamical mean-field approach, we compute the nuclear spin polarization distribution with and without the quadrupolar coupling. We find that while hyperfine interactions drive dynamic nuclear polarization and mode-locking, quadrupolar couplings counteract these effects. The tension between these mechanisms is imprinted on the steady-state electron spin evolution, providing a way to measure the importance of quadrupolar interactions in a quantum dot. Our results show that higher-spin effects such as quadrupolar interactions can have a significant impact on the generation of dynamic nuclear polarization and how it influences the electron spin evolution.

An Electronic Correlation Approach to the Metal–Insulator Transition in the Half-Metallic Sr2FeMoO6Compound Doped With W

The ferromagnetic double perovskite Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> FeMoO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> (SFMO) system with half-metallicity and fairly high Curie temperature points to the possibility of designing spintronics materials operating at room temperature. On the other hand, the double perovskite Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> FeWO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> is an antiferromagnetic insulator with the W(5d) states located at high energies and also with completely different magnetic and electronic properties than the ferromagnetic SFMO. The ferromagnetism and half-metallicity in SFMO have been explained within a strongly correlated picture, in which Fe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> (3d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> ) are localized spins in a high-spin S = 5/2 configuration and Mo <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5+</sup> (4d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> ) cores have one itinerant electron per formula unit (f.u.), which can hop to Fe sites only with an orientation antiparallel to that of the localized spin, thus stabilizing a ferromagnetic arrangement of local spins and fully opposite spin-polarized itinerant electrons. In this work, we study the effect of cationic doping on the behavior of \textT <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> in SFMO with the Mo ions replaced by W ions, which leads to a metal-insulator transition. We use Green's function technique and the renormalization perturbation expansion method, in which the localized Fe spins and conduction Mo electrons interact via a double-exchange-type mechanism and the Hubbard model. Electronic correlations among the conduction electrons are included within a dynamical mean-field approach. Our results show a metal-insulator transition for W doping around x=0.2 in good agreement with experiments.

Pair-correlation functions and density-modulated states in electron–hole bilayer: thermal and mass-asymmetry effects

We have studied the effect of temperature and electron–hole mass-asymmetry on pair-correlation functions (PCFs) of a coupled electron–hole bilayer, treating correlations dynamically using the dynamical self-consistent mean-field approach of Singwi, Tosi, Land, and Sjolander. Taking a fixed electron–hole effective mass ratio $$m_h^*/m_e^*=5$$ , both intra- and interlayer static PCFs are calculated for their dependence on carrier density $$r_{se}$$ , temperature $$\tau _e$$ , and interlayer spacing d. Besides, the static wavevector-dependent density susceptibility is obtained to probe the role of these effects on the hitherto existence of density-modulated phases in the bilayer. We find that thermal effects in overall make correlations weaker, but the mass-asymmetry results in stronger correlations both within and across the layers, with the effect being most pronounced in the holes layer. In the strong coupling regime (i.e., large $$r_{se}/\tau _e d$$ ), the intra- and interlayer PCFs show pronounced in-phase periodic oscillations, typical of a spatially localized phase in the bilayer. Correspondingly, the in-phase component of static density susceptibility is seen to exhibit in the close approach of two layers an apparently diverging peak at a wavevector coincident with the location of sharp peak in the static structure factor, implying the emergence of a density-modulated phase in the bilayer. Parallel to the zero-temperature study, the charge-density-wave (CDW) phase is found to dominate at higher densities, with a cross-over to the Wigner crystal (WC) phase below a critical density. As an interesting result, we find that while thermal effects tend to oppose the formation of density-modulated phase, the electron–hole mass-asymmetry boosted correlations favour it, with the two effects almost cancelling out at $$\tau _e=0.125$$ , thus resulting in the CDW-WC cross-over at nearly the same critical density as for a zero-temperature mass-symmetric electron–hole bilayer. Our prediction of coupled WC phase is found to be in qualitative agreement with path-integral Monte Carlo simulations.

Proton fraction in neutron star matter: dynamical mean-field approach

Dynamical mean field theory (DMFT) is used to study neutron matter, both with and without admixture of the proton fraction. The system is approximated by the lattice Hubbard model. The corresponding equation of state as a function of temperature/density/asymmetry is investigated. The results are compared with the standard mean field (MF) approach where the effect of local correlations is neglected. Whereas the influence of the correlations on the properties of a pure neutron matter is found to be moderate, it becomes strong when the proton admixture is taken into account. In particular, we calculate the proton fraction, energy density and pressure in outer core of neutron stars, taking into account the beta equilibrium condition. The DMFT predicts that the proton fraction is several times the MF based calculations, whereas the DMFT results for energy density and pressure are 30%–40% lower than the corresponding MF estimates. Physical implications of our findings for a neutron star dynamics are discussed.

Dynamical correlation enhanced orbital magnetization in VI3

The effect of electronic correlations on the orbital magnetization in real materials has not been explored beyond a static mean-field level. Based on the dynamical mean-field theory, the effect of electronic correlations on the orbital magnetization in layered ferromagnet ${\mathrm{VI}}_{3}$ has been studied. A comparison drawn with the results obtained from density-functional theory calculations robustly establishes the crucial role of dynamical correlations in this case. In contrast to the density-functional theory that leads to negligible orbital magnetization in ${\mathrm{VI}}_{3}$, in dynamical mean-field approach the orbital magnetization is greatly enhanced. Further analysis shows that this enhancement is mainly due to the enhanced local circulations of electrons, which can be attributed to a better description of the localization behavior of correlated electrons in ${\mathrm{VI}}_{3}$. The conclusion drawn in our paper could be applicable to a wide range of layered materials in this class.

Anisotropy of electronic correlations: On the applicability of local theories to layered materials

Besides the chemical constituents, it is the lattice geometry that controls the most important material properties. In many interesting compounds, the arrangement of elements leads to pronounced anisotropies, which reflect into a varying degree of quasi two-dimensionality of their low-energy excitations. Here, we start by classifying important families of correlated materials according to a simple measure for the tetragonal anisotropy of their ab initio electronic (band) structure. Second, we investigate the impact of a progressively large anisotropy in driving the non-locality of many-body effects. To this end, we tune the Hubbard model from isotropic cubic in three dimensions to the two-dimensional limit and analyze it using the dynamical vertex approximation. For sufficiently isotropic hoppings, we find the self-energy to be well separable into a static non-local and a dynamical local contribution. While the latter could potentially be obtained from dynamical mean-field approaches, we find the former to be non-negligible in all cases. Further, by increasing the model-anisotropy, we quantify the degree of quasi two-dimensionality which causes this "space-time separation" to break down. Our systematic analysis improves the general understanding of electronic correlations in anisotropic materials, heterostructures and ultra-thin films, and provides useful guidance for future realistic studies.

Dynamical chaotic phases and constrained quantum dynamics

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the noncommutativity of observables. Motivated by recent progress in the experimental control of quantum systems, we propose a framework for the implementation of quantum constraints based on the idea of work protocols, which are dynamically engineered to enforce the constraints. As a proof of principle, we consider the dynamical mean-field approach of the many-body quantum spherical model, which takes the form of a quantum harmonic oscillator plus constraints on the first and second moments of one of its quadratures. The constraints of the model are implemented by the combination of two work protocols, coupling together the first and second moments of the quadrature operators. We find that such constraints affect the equations of motion in a highly nontrivial way, inducing nonlinear behavior and even classical chaos. Interestingly, Gaussianity is preserved at all times. A discussion concerning the robustness of this approach to possible experimental errors is also presented.

Ferromagnetic transition and spin fluctuations in diluted magnetic semiconductors

The magnetic properties over a wide range of temperatures in diluted magnetic semiconductors (DMSs) are discussed in the framework of the Kondo lattice model with magnetic impurity disorder. In the approach of dynamical mean-field theory, a set of self-consistent equations has been derived to specify single-particle Green functions. Analytical expressions of the static magnetic susceptibility and the ${B}_{1g}$ channel Raman response are then delivered. Inspecting for signatures of an itinerant carrier density of states and magnetization, we have identified a stable ferromagnetic (FM) state at low temperature. With increasing temperature, thermal fluctuations diminish the ordered state and the system favors a paramagnetic (PM) phase. Tracking and tracing different model parameters, the FM-PM transition phase diagram has been constructed. Spin fluctuations in the PM state have been pointed out in the behaviors of the self-energies, the static magnetic susceptibility, and the Raman scattering. Analyzing the properties of the ${B}_{1g}$ channel Raman response, we have attributed a formation of magnetic polarons in the PM state. The magnetic polaron scenario in a wide range of temperatures has been then intensively discussed. For the first time, both the static magnetic susceptibility and the ${B}_{1g}$ Raman response have been combined together to discuss the magnetic properties in DMSs compactly based on the dynamical mean-field approach.

Relativistic theory of two-photon photoemission from ferromagnetic materials

A fully relativistic theory of angle-resolved two-photon photoemission for ferromagnetic materials is derived from the general theory of pump-probe photoemission that is based on the Keldysh formalism. Two-photon photoemission spectroscopy is a widely used analytical tool to study nonequilibrium phenomena in nonmagnetic as well as in magnetic solids, as for example ultrafast demagnetization processes. Our theoretical approach aims at a quantitative description of the time-dependent spectroscopic properties of specific solid systems under consideration, and it allows for the inclusion of static correlation effects via the local spin-density and dynamical mean-field theory electronic structure approach. To this end we follow Pendry's one-step theory of the photoemission process as closely as possible and make extensive use of concepts of relativistic multiple - scattering theory within the layer-Korringa-Kohn-Rostoker method in order to guarantee angular resolution in the spectroscopic calculations. As usual the final state of the two-photon photoemission process is represented by a time-reversed low-energy electron diffraction state. The formalism allows for a quantitative calculation of the time-dependent photocurrent for moderately correlated systems like simple ferromagnetic metals. A first application to the Fe(100) surface is discussed in detail.

Dynamical mean-field theoretical approach to explore the temperature-dependent magnetization in Ta-doped TiO2

TiO2 has, in recent years, become a hot subject as it holds a promise for spintronic application. Recent experimental study on anatase Ti1−xTaxO2 (x ~ 0.05) thin films shows that the system changes from non-magnetic to ferromagnetic due to Ti vacancies that are formed when a small percentage of Ti atoms are substituted by Ta. Motivated by those results that reveal the ferromagnetic phase at room temperature, we conduct a theoretical study on the temperature-dependent magnetization and the Currie temperature of that system. We hypothesize that when several Ti vacancies are formed in the system, each of them induces a local magnetic moment, then such moments couple each other through Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, forming a ferromagnetic order. To study the temperature dependence of the magnetization and predict the Curie temperature, we construct a tight-binding based Hamiltonian for this system and use the method of dynamical mean-field theory to perform calculations for various temperatures. Our work is still preliminary. The model and method may need further improvement to be consistent with known existing facts. We present our preliminary results to show how the present model works.

Mott transition, spin-orbit effects, and magnetism in Ca2RuO4

In this work, we study the effects of spin-orbit and Coulomb anisotropy on the electronic and magnetic properties of the Mott insulator ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$. We use the local-density approximation + dynamical mean-field approach and spin-wave theory. We show that, contrary to a recent proposal, the Mott metal-insulator transition is not induced by the spin-orbit interaction. We confirm that, instead, it is mainly driven by the change in structure from long to short $\mathbf{c}$-axis layered perovskite. We show that the magnetic ordering and the anisotropic Coulomb interactions play a small role in determining the the size of the gap. The spin-orbit interaction turns out to be essential for describing the magnetic properties. It not only results in a spin-wave gap, but it also enlarges significantly the magnon bandwidth.

Effect of the Hamiltonian parameters on Blume-Capel Ising ferromagnet system with single-ion anisotropy

The dynamic mean-field approach have been utilized to investigate effect of the Hamiltonian parameters on the dynamic magnetic properties of a Blume-Capel Ising ferromagnet system in two dimensions, comprising a ferromagnetic spins S = ±3/2, ±1/2. The effect of the single-ion anisotropy (d) and the frequency (w) of the external oscillating magnetic field on the dynamic hysteresis cycle (DHC) are explored in detail. It is found that the DHC increases as the d increases and at a certain d, the DHC decreases with increasing the d. Furthermore, the DHC is very sensitive to changes in the w. We also examine the effect of the w on the dynamic phase diagrams and observe the dynamic phase diagrams illustrate richer dynamic critical behavior for higher values of w than for lower values.

Transport Properties of Metallic Ruthenates: ADFT+DMFTInvestigation

We present a systematical theoretical study on the transport properties of an archetypal family of Hund's metals, Sr_{2}RuO_{4}, Sr_{3}Ru_{2}O_{7}, SrRuO_{3}, and CaRuO_{3}, within the combination of first principles density functional theory and dynamical mean field theory. The agreement between theory and experiments for optical conductivity and resistivity is good, which indicates that electron-electron scattering dominates the transport of ruthenates. We demonstrate that in the single-site dynamical mean field approach the transport properties of Hund's metals fall into the scenario of "resilient quasiparticles." We explain why the single layered compound Sr_{2}RuO_{4} has a relative weak correlation with respect to its siblings, which corroborates its good metallicity.

Orbital magnetism of ultracold fermionic gases in a lattice: Dynamical mean-field approach

We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically-ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically-ordered phases, which provides quantitative predictions for on-going and future experiments aiming at approaching and studying long-range ordered states in optical lattices.

Generalized mean-field approach to simulate the dynamics of large open spin ensembles with long range interactions

We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we improve the numerical approximation of the full master equation by including pair correlations at any distance. This truncations enable us to drastically increase the number of spins in our numerical simulations from about ten spins in case of the full quantum model to several ten-thousands in the mean-field approximation and a few hundreds if pair correlations are included. Extensive numerical tests help us identify interaction strengths and geometric configurations where these approximations perform well and allow us to state fairly simple error estimates. By simulating systems of increasing size we show that in one and two dimensions we can include as many spins as needed to capture the properties of infinite size systems with high accuracy, while in 3D the method does not converge to desired accuracy within the system sizes we can currently implement. Our approach is well suited to give error estimates of magic wavelength optical lattices for atomic clock applications and corresponding super radiant lasers.

Theory of Spin-State Selective Nonlocal Screening in Co 2p X-ray Photoemission Spectrum of LaCoO3

The Co 2p X-ray photoemission spectrum (XPS) of LaCoO3 is investigated using a dp model simulating Co 3d and O 2p orbitals by means of a dynamical mean-field approach under the perovskite crystal structure. Across the spin-state transition from the low-spin to the high-spin state, the Co 2p3/2 main-line structure is substantially changed beyond expectation of a CoO6 cluster model calculation. In addition to the Coulombic multiplet effect, the origin of the spectral change is attributed to the nonlocal screening (NLS) from the correlated 3d band located on the top of the valence band to the core-excited Co site in the final state, where the NLS is practically active only for the high-spin state. The spin-state selectivity of the NLS is closely related to not only the spin state of the core-excited Co ion but also the spin and orbital character of the occupied Co 3d band in crystals. We emphasize that the Co 2p XPS can be an informative probe to investigate the spin state of Co ions in Co oxides, such as LaCoO3.

Cluster extended dynamical mean-field approach and unconventional superconductivity

The extended dynamical mean field theory has played an important role in the study of quantum phase transitions in heavy fermion systems. In order to incorporate the physics of unconventional superconductivity, we develop a cluster version of the extended dynamical mean field theory. In this approach, we show how magnetic order and superconductivity develop as a result of inter-site spin exchange interactions, and analyze in some detail the form of correlation functions. We also discuss the methods that can be used to solve the dynamical equations associated with this approach. Finally, we consider different settings in which our approach can be applied, including the periodic Anderson model for heavy fermion systems.