Dynamical Mean-field Approximation Research Articles

Coupled plasmon-LO-phonon modes in the ground state of a GaAs-based electron-electron biwire system

We study the coupled plasmon-longitudinal optical-phonon (pl-LO-ph) modes in a GaAs-based electron-electron (e-e) biwire system at absolute zero within the dynamic mean-field approximation of Singwi and others (popularly known as the qSTLS theory). Here, in addition to the standard electron-electron (e-e) interactions, we also take into account the electron-phonon (e-ph) coupling and calculate pl-LO-ph modes at some selected values of wire-width, inter-wire separation and electron number density. The coupled modes are found to resonantly split into eight branches, four of which lie outside and four inside the electron-hole (e-h) pair continuum. Out of four branches which exist above the e-h pair continuum, two are plasmon-like modes having energies below than that of transverse optical (TO) phonons, and the other two are phonon-like modes having energies above longitudinal optical (LO) phonons. Additionally, we compare the plasmon-like modes with true plasmons (resulting only from the typical e-e interactions) and note that the e-ph coupling softens the true plasmon modes.

Induced Wigner crystallization in a coupled electron-hole quantum wire system at finite-temperature

We explore the possibility of induced Wigner crystallization in a coupled electron-hole (e-h) quantum wire system at finite-temperature T by calculating the intra- and inter-wire static structure factors in the dynamic mean-field approximation of Singwi et al (the qSTLS theory). We find that owing to the dynamics of severely correlated particles, the e-h system may favour an induced phase transition from quantum liquid to the Wigner crystal state at a non-zero T and sufficiently low particle (electron/hole) number density in the close proximity of two wires. On the other hand, the static STLS approximation does not predict such phase transition due to complete neglect of the dynamics of particle correlations.

Optical conductivity of the two-dimensional Hubbard model: Vertex corrections, emergent Galilean invariance, and the accuracy of the single-site dynamical mean field approximation

We compute the frequency-dependent conductivity of the two-dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single-site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the model exhibits an emergent Galilean invariance. The DMFT approximation also becomes qualitatively inaccurate very near half filling if nesting is important.

Ground-state properties of an electron-phonon coupled quantum wire within the dynamic mean-field approximation

We investigate the ground-state properties of an electron-phonon (e-ph) coupled quantum wire in which the effect of coupling between longitudinal optical (LO) phonons and the wire electrons is considered, in addition to the conventional electron-electron (e-e) interactions. The e-ph coupling is included through the Fröhlich interaction potential and the dynamics of electron correlations using the quantum (dynamic) version of self-consistent mean-field approximation of Singwi et al (the qSTLS approach). Numerical results for static structure factor, pair-correlation function and static density susceptibility are presented over a wide range of electron number density parameter r s . We find that the electrons undergo Wigner crystallization at a critical electron density parameter r s c owing to the dynamics of severely correlated electrons. Notably at a fixed wire width, the inclusion of e-ph coupling tends to increase the value of r s c significantly in comparison to a situation in which only the e-e interactions are considered. Besides this, we compute the plasmon-phonon (pl-ph) coupled modes and the energy contribution of e-ph interactions (E e−ph ) to the ground-state energy of the quantum wire, also known as polaronic energy. We find that pl-ph coupled modes resonantly split into two branches, and ∣E e−ph ∣ monotonically increases with rise in r s then becomes almost constant as . Wherever interesting, we compare our results with the static STLS theory and the lattice regularized diffusion Monte Carlo (LRDMC) simulation data of Casula et al.

Magnetic response trends in cuprates and the t−t′ Hubbard model

We perform a systematic study of static and dynamical magnetic properties of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model in a parameter regime relevant for high-temperature superconducting cuprates. We adopt as solution method the dynamical mean-field theory approximation and its real-space cluster extension. Our results show that large ${t}^{\ensuremath{'}}/t$ suppresses incommensurate features and eventually leads to ferromagnetic instabilities for sufficiently large hole doping $x$. We identify isosbestic points which separate parts of the Brillouin zone with different scaling behaviors. Calculations are compared to available nuclear magnetic resonance, nuclear quadrupole resonance, inelastic neutron scattering, and resonant inelastic x-ray scattering experiments. We show that while many trends are correctly described, e.g., the evolution with $x$, some aspects of the spin-lattice relaxation rates can apparently only be explained invoking accidental cancellations. In order to capture the material dependence of magnetic properties in full, it may be necessary to add further degrees of freedom.

The NERA model incorporating cellular automata approach and the analysis of the resulting induced stochastic mean field

A stochastic process depicting the spreading dynamics of illicit drug consumption in a given population forms the crux of this work. A probabilistic cellular automaton (PCA) model is developed to examine the effects of the social interactions between nonusers and drug users. The model, called NERA, comprises four classes of individuals, namely, nonuser (N), experimental user (E), recreational user (R), and addict user (A). The stochastic process evolves in time by local transition rules. By means of dynamical simple mean field approximation, a nonlinear system of differential equations illustrating the dynamics of the PCA is obtained. The existence and uniqueness of a positive solution of the model is established, and the fixed points of the system are sought to perform the stability analysis. Furthermore, a stochastic mean field (SMF) approach to the NERA system is introduced. SMF extends the latter model to integrate the stochastic behaviour of drug consumers in a given environment. The SMF system is shown to exhibit a unique global solution which is stochastically ultimately bounded. Simulations of the cellular automaton and mean field analysis are used to study the evolution of the model. Verification and validation are carried out using data available on the consumption of cannabis in the state of Washington (Darnell and Bitney in $${I}-502$$ evaluation and benefit-cost analysis: second required report, Washington state institute for public policy. Technical Report, 2017). These numerical experiments confirm that the NERA model can help in the analysis and quantification of the spatial dynamics of illicit drug usage in a given society and eventually provide insight to policy-makers on different steps to be taken to curb this social epidemic.

Dynamic hysteresis and compensation behaviors of the bilayer Blume–Capel model under an oscillating magnetic field

Dynamic compensation and hysteresis characteristics of Blume–Capel (BC) model under an oscillating magnetic field have been studied within the dynamic mean field approximation. Spin-1 ferro-antiferromagnetic system Hamiltonian contains bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on a bilayer square lattice. Benefiting from the thermal variations of the total magnetization, we find the L-, Q-, R- and S-type compensation behaviors in the system. According to our results, the system does not represent dynamic compensation behavior when it only includes one interaction parameter. We found that the existence of compensation temperatures and hysteresis properties strongly depends on crystal field interactions. It has also been shown that for the paramagnetic phase of the system, single hysteresis behaviors may occur. Finally, the obtained results are compared with some experimental and theoretical results and found in a qualitatively good agreement.

Spin-imbalance-induced transverse magnetization in the Hofstadter-Hubbard model

The fermionic, time-reversal invariant Hofstadter-Hubbard model with a population difference between the two spin states is investigated. In the strongly interacting regime, where the system can be described by an effective spin model, we find an exotic spin structure by means of classical Monte-Carlo calculations. Remarkably, this spin structure exhibits a transverse net magnetization perpendicular to the magnetization induced by the population imbalance. It is thus inherently different from canted antiferromagnetism. We further investigate effects of quantum fluctuations within the dynamical mean-field approximation and obtain a rich phase diagram including ferromagnetic, anti-ferromagnetic, ferrimagnetic, and transverse magnetization phases.

Quantum phase transitions in the two dimensional ionic-Hubbard model

We employ the dynamical mean field approximation to study the effects of ionic potential (Δ) on the square lattice Hubbard model. At half-filling when the staggered potential (Δ) dominates the on-site Hubbard interaction (U), the system is in the band insulator phase. We find that competition between U and Δ can suppress the gap to zero and leading to an intermediate metallic region. At the large-U limit, we identify a Mott insulator phase where the gap opens again and increases upon increasing the Hubbard interaction U. For U ≤ 9t and Δ ≈ 0 the phase of the system is metallic, but for larger U the system is in the Mott insulator phase.

Finite-temperature correlations in a two-dimensional electron gas within a dynamical self-consistent mean-field approximation

We have studied the effect of temperature on density-density correlations in a two-dimensional quantum electron gas by using the dynamical Singwi-Tosi-Land-Sjölander (STLS) theory. Static correlation functions viz. structure factor S(q; T), pair-correlation function g(r; T), and static density susceptibility χ(q, 0; T) are calculated over a wide range of temperature and electron density. The inclusion of the dynamics of correlations is found to cause a strong peak in S(q; T) at q ∼ 2.5kF for low densities. Correspondingly, there develops a sharp peak in χ(q, 0; T) that diverges below a critical density. This divergence is interpreted as a precursor of transition to finite-temperature Wigner crystal state. Rise in temperature tends to oppose the crystallization, with critical transition density decreasing with temperature. It is rather found that the dynamical correction to the conventional (static) STLS theory becomes small at a sufficiently high temperature. We have also calculated the plasmon dispersion for the GaAs quantum well based electron system and found that, except at ultra-low densities, agreement with the experimental data of Hirjibehedin et al. is reasonably good. Our results show a red shift in plasmon frequency over the predictions of the STLS and dynamical Hubbard approaches.

Temperature dependence of the NMR Knight shift in pnictides: Proximity to a van Hove singularity

The unconventional temperature variation of the Knight shift (static spin susceptibility) that has been observed in Fe-based superconductors AFe$_2$As$_2$ (A = K, Rb, Cs) is explained in terms of proximity to a van Hove singularity. Using the Hubbard model we show that when the Fermi energy is in the vicinity of a van Hove singularity, a downturn in spin susceptibility occurs as the temperature is lowered. This behavior is characterized by a temperature, $T^*$, which is determined by the difference in energy between the Fermi level and the van Hove singularity. When vertex corrections are taken into account in a dynamical mean-field approximation, the effect of correlations amplifies the relative drop in the Knight shift and moves $T^*$ to lower temperatures.

Matching DMFT calculations with photoemission spectra of heavy fermion insulators: universal properties of the near-gap spectra of SmB6

Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB6).

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological “particles” move along some kind of “tracks”. The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Inference for dynamics of continuous variables: the extended Plefka expansion with hidden nodes

We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks underlying many cellular and metabolic processes are important realizations of such a scenario as typically one is interested in reconstructing the time evolution of unobserved chemical concentrations starting from the experimentally more accessible ones. We present an application to this problem of a novel dynamical mean field approximation, the extended Plefka expansion, which is based on a path integral description of the stochastic dynamics. As a paradigmatic model we study the stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings. The resulting joint distribution is known to be Gaussian and this allows us to fully characterize the posterior statistics of the hidden nodes. In particular the equal-time hidden-to-hidden variance—conditioned on observations—gives the expected error at each node when the hidden time courses are predicted based on the observations. We assess the accuracy of the extended Plefka expansion in predicting these single node variances as well as error correlations over time, focussing on the role of the system size and the number of observed nodes.

Theoretical exploration of optical response of Fe3O4-reduced graphene oxide nanoparticle system within dynamical mean-field theory

We theoretically investigate the optical conductivity and its related optical response of Fe3O4-reduced graphene oxide (rGO) nanoparticle system. Experimental data of magnetization of the Fe3O4-rGO nanoparticle system have shown that the saturation magnetization can be enhanced by controlling the rGO content with the maximum enhancement reached at the optimal rGO content of about 5 weight percentage. We hypothesize that the magnetization enhancement is due to spin-flipping of Fe ions at tetrahedral sites induced by oxygen vacancies at the Fe3O4 nanoparticle boundaries. These oxygen vacancies are formed due to adsorption of oxygen atoms by rGO flakes around the Fe3O4 nanoparticle. In this study, we aim to explore the implications of this effect to the optical response of the system as a function of the rGO content. Our model incorporates Hubbard-repulsive interactions between electrons occupying the e g orbitals of Fe3+ and Heisenberg-like interactions between electron spins and spins of Fe3+ ions. We treat the relevant interactions within mean-field and dynamical mean-field approximations. Our results are to be compared with the existing experimental reflectance data of Fe3O4 nanoparticle system.

Electron interactions, spin-orbit coupling, and intersite correlations in pyrochlore iridates

We perform combined density functional and dynamical mean-field calculations to study the pyrochlore iridates Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$ and Eu$_2$Ir$_2$O$_7$. Both single-site and cluster dynamical mean-field calculations are performed and spin-orbit coupling is included. Paramagnetic metallic phases, antiferromagnetic metallic phases with tilted Weyl cones and antiferromagnetic insulating phases are found. The magnetic phases display all-in/all-out magnetic ordering, consistent with previous studies. Unusually for electronically three dimensional materials, the single-site dynamical mean-field approximation fails to reproduce qualitative material trends, predicting in particular that the paramagnetic phase properties of Y$_2$Ir$_2$O$_7$ and Eu$_2$Ir$_2$O$_7$ are almost identical, although in experiments the Y compound has a much higher resistance than the Eu compound. This qualitative failure is attributed to the importance of intersite magnetic correlations in the physics of these materials.

Dynamic Properties of Kinetic Spin-3/2 Ising Ferromagnetic Model in the Presence of the Crystal and External Oscillating Magnetic Fields

The kinetic spin-3/2 Ising system in the presence of crystal and external oscillating magnetic fields on the triangular lattice (TL) is examined within the mean-field approximation and the Glauber-type stochastic dynamics, namely dynamic mean-field approximation (DMFA). First, the dynamic equations describing the behavior of the system are derived for the TL. Then, the dynamic equations are solved numerically to obtain the dynamic hysteresis curves of the kinetic spin-3/2 Ising ferromagnetic system, which strongly depend on the Hamiltonian parameters. Moreover, the dynamic behaviors of the coercivity and remanent magnetizations are studied depending on the temperature, crystal field and frequency of the oscillating external magnetic field. Finally, the results are compared with some experimental and theoretical studies and a qualitatively good overall agreement is observed

Dynamic magnetic hysteresis properties of two-dimensional ferrimagnetic structures containing high-spin (S = 5/2) and low-spin (S = 1/2)

ABSTRACTThe dynamic hysteresis behaviors of a containing high spin-5/2 and low spin-1/2 Ising ferrimagnetic system on a square lattice are studied by using the dynamic mean-field approximation. The influences of the temperature, the single-ion anisotropy and the frequency on dynamic hysteresis behaviors are investigated in detail. Somewhat characteristic behaviors are found, such as the presence of triple hysteresis loop for appropriate values of the crystal field or temperature. Besides, we observed that, hysteresis loop area and phase transition points are very sensitive to changes in frequency and thus have profound importance in device application.

Dynamic Magnetic Hysteresis Properties in a Two-Dimensional Mixed Ising System Designed with Integer and Half-Integer Spins

Dynamic magnetic hysteresis properties in a two-dimensional mixed Ising system designed with integer and half-integer spins, namely spin-1 and spin-5/2, are investigated comprehensively on the basis of the mean-field approximation and the Glauber-type stochastic dynamics, namely dynamic mean-field approximation (DMFA). In particular, we examine the effect of Hamiltonian parameters on dynamic hysteresis properties. As a result of this examination, some characteristic hysteresis behaviors are obtained, such as the existence of single, double and triple hysteresis. Moreover, we study to obtain coercive field and remanent magnetization. Our results are compared with some experimental and theoretical works to find a qualitatively good agreement.

Ferromagnetism and correlation strength in cubic barium ruthenate in comparison to strontium and calcium ruthenate: A dynamical mean-field study

We present density functional plus dynamical mean field studies of cubic BaRuO$_3$ using interaction parameters previously found to be appropriate for the related materials CaRuO$_3$ and SrRuO$_3$. The calculated variation in transition temperature between the Ba and Sr compounds is consistent with experiment, confirming the assignment of the compounds to the Hund's metal family of materials, and also confirming the appropriateness of the values for the interaction parameters previously estimated and the appropriateness of the single-site dynamical mean field approximation for these materials. The results provide insights into the origin of magnetism and the role of the van Hove singularity in the physics of Hund's metals.