Mean-field Theory Research Articles

Single-site DFT+DMFT for vanadium dioxide using bond-centered orbitals

We present a combined density-functional theory and single-site dynamical mean-field theory (DMFT) study of vanadium dioxide (VO2) using an unconventional set of bond-centered orbitals as the basis of the correlated subspace. VO2 is a prototypical material undergoing a metal-insulator transition (MIT), hosting both intriguing physical phenomena and the potential for industrial applications. With our choice of correlated subspace basis, we investigate the interplay of structural dimerization and electronic correlations in VO2 in a computationally cheaper way compared to other state-of-the-art methods, such as cluster DMFT. Our approach allows us to treat the rutile and M1 monoclinic VO2 phases on an equal footing and to vary the dimerizing distortion continuously, exploring the energetics of the transition between the two phases. The choice of basis presented in this work hence offers a complementary view on the long-standing discussion of the MIT in VO2 and suggests possible future extensions to other similar materials hosting molecular-orbital-like states. Published by the American Physical Society 2024

Dielectric Boundary Force for the Minimization of the Mean-Field Electrostatic Free-Energy Functional Including the Ionic Size Effect

The generalized Poisson–Boltzmann equation with the uniform ionic size is investigated. In mean-field theory, the ionic size effect is added by modifying the entropy effect of solvent molecules in the electrostatic free-energy functional of ion concentrations. Taking minimization of the mean-field electrostatic free-energy functional including the ionic size effect with respect to the ion concentrations, the minimum free-energy is obtained (see (4.6) in Li [(2009a) “Continuum electrostatics for ionic solutions with non-uniform ionic sizes,” Nonlinearity 22(4), 811–833]. Maximizing the minimum free-energy with respect to the electrostatic potential determines the generalized Poisson–Boltzmann equation. By the definition of shape derivative, the first variation of this minimum free-energy with respect to variation of the dielectric boundary is derived. Thus, the dielectric boundary force of an ionic solution with multiple ionic species with the uniform ionic size is obtained.

Optimization of fluorinated phenyl azides as universal photocrosslinkers for semiconducting polymers

Fluorinated phenyl azides (FPA) enable photo-structuring of π-conjugated polymer films for electronic device applications. Despite their potential, FPAs have faced limitations regarding their crosslinking efficiency, and more importantly, their impact on critical semiconductor properties, such as charge-carrier mobility. Here, we report that azide photolysis and photocrosslinking can achieve unity quantum efficiencies for specific FPAs. This suggests preferential nitrene insertion into unactivated C‒H bonds over benzazirine and ketenimine reactions, which we attribute to rapid interconversion between the initially formed hot states. Furthermore, we establish a structure‒activity relationship for carrier mobility quenching. The binding affinity of FPA crosslinker to polymer π-stacks governs its propensity for mobility quenching in both PM6 and PBDB-T used as model conjugated polymers. This binding affinity can be suppressed by FPA ring substitution, but varies in a non-trivial way with π-stack order. Utilizing the optimal FPA, photocrosslinking enables the fabrication of morphology-stabilized, acceptor-infiltrated donor polymer networks (that is, PBDB-T: ITIC and PM6: Y6) for solar cells. Our findings demonstrate the exceptional potential of the FPA photochemistry and offer a promising approach to address the challenges of modelling realistic molecular interactions in complex polymer morphologies, moving beyond the limitations of Flory‒Huggins mean field theory.

Half-Metallic Transport and Spin-Polarized Tunneling through the van der Waals Ferromagnet Fe4GeTe2.

We examine the coherent spin-dependent transport properties of the van der Waals (vdW) ferromagnet Fe4GeTe2 using density functional theory combined with the nonequilibrium Green's function method. Our findings reveal that the conductance perpendicular to the layers is half-metallic, meaning that it is almost entirely spin-polarized. This property persists from the bulk to a single layer, even under significant bias voltages and with spin-orbit coupling. Additionally, using dynamical mean field theory for quantum transport, we demonstrate that electron correlations are important for magnetic properties but minimally impact the conductance, preserving almost perfect spin-polarization. Motivated by these results, we then study the tunnel magnetoresistance (TMR) in a magnetic tunnel junction consisting of two Fe4GeTe2 layers with the vdW gap acting as an insulating barrier. We predict a TMR ratio of ∼500%, which can be further enhanced by increasing the number of Fe4GeTe2 layers in the junction.

Accuracy of discrete- and continuous-time mean-field theories for epidemic processes on complex networks.

Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these approaches, and the choice is usually based on one's expertise or methodological convenience, on the other hand, a detailed analysis of the differences is necessary to guide the proper choice of one or another approach. We tackle this problem by investigating both discrete- and continuous-time mean-field theories for the susceptible-infected-susceptible (SIS) epidemic model on random networks with power-law degree distributions. We compare the discrete epidemic link equations(ELE) and continuous pair quenched mean-field (PQMF) theories with the corresponding stochastic simulations, both theories that reckon pairwise interactions explicitly. We show that ELE converges to the PQMF theory when the time step goes to zero. We performed an epidemic localization analysis considering the inverse participation ratio (IPR). Both theories present the same localization dependence on network degree exponent γ: for γ<5/2 the epidemics are localized on the maximum k-core of networks with a vanishing IPR in the infinite-size limit while, for γ>5/2, the localization happens on hubs that do not form a densely connected set and leads to a finite value of the IPR. However, the IPR and epidemic threshold of ELE depend on the time-step discretization such that a larger time step leads to more localized epidemics. A remarkable difference between discrete- and continuous-time approaches is revealed in the epidemic prevalence near the epidemic threshold, in which the discrete-time stochastic simulations indicate a mean-field critical exponent θ=1 instead of the value θ=1/(3-γ) obtained rigorously and verified numerically for the continuous-time SIS on the same networks.

Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum

Abstract The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. A periodic evolution for the ground state shapes is shown with the neutron number, i.e., spherical shapes at shell closures N=126, 184, 258, and prolate dominated shapes between them. In analogy to the shape evolution, the inner fission barriers also exhibit a periodic behavior: peaks at the shell closures and valleys in the mid-shells. The triaxial effect to the inner fission barrier is evaluated using the triaxial relativistic mean field calculations plus a simple BCS method for pairing. With the triaxial correction included, good consistency in the inner barrier heights is found with the available empirical data.&amp;#xD;Besides, the evolution from the proton to the neutron drip line is in accord with the results by the multi-dimensionally constrained relativistic mean field theory. A flat valley in the fission barrier height is predicted around the neutron-rich nucleus 318U which may play a role of fission recycling in the astrophysical r-process nucleosynthesis.&amp;#xD;

Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the &amp;#x3BB;&amp;#x3D5;4 model

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field &amp;#x03D5;(x) locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional &amp;#x03BB;&amp;#x03D5;4 terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling &amp;#x03BB;. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the &amp;#x03BB;&amp;#x03D5;4 QFT.

Quantifying the U 5f covalence and degree of localization in U intermetallics

A procedure for quantifying the U 5f electronic covalency and degree of localization in U intermetallic compounds is presented. To this end, bulk sensitive hard and soft x-ray photoelectron spectroscopy were utilized in combination with density-functional theory (DFT) plus dynamical mean-field theory (DMFT) calculations. The energy dependence of the photoionization cross sections allows the disentanglement of the U 5f contribution to the valence band from the various other atomic subshells so the computational parameters in the DFT+DMFT can be reliably determined. Applying this method to UGa2 and UB2 as model compounds from opposite ends of the (de)localization range, we have achieved excellent simulations of the valence band and core-level spectra. The width in the distribution of atomic U 5f configurations contributing to the ground state, as obtained from the calculations, quantifies the correlated nature and degree of localization of the U 5f. The findings permit answering the longstanding question why different spectroscopic techniques give seemingly different numbers for the U 5f valence in intermetallic U compounds. Published by the American Physical Society 2024

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions.

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

Dynamic Behavior of Poly(N-isopropylmethacrylamide) in Neat Water and in Water/Methanol Mixtures.

We investigate the collective dynamics of thermoresponsive polymer poly(N-isopropylmethacrylamide) (PNIPMAM) in aqueous solution and in water/methanol mixtures in the one-phase region. In neat water, the polymer concentration c is varied in a wide range around the overlap concentration c*, that is estimated at 23 g L-1. Using dynamic light scattering (DLS), two decays ("modes") are consistently observed in the intensity autocorrelation functions for c = 2-150 g L-1 with relaxation rates which are proportional to the square of the momentum transfer. Below c*, these are attributed to the diffusion of single chains and to clusters from PNIPMAM that are formed due to hydrophobic interactions. Above c*, they are assigned to the diffusion of the chain segments between overlap points and to long-range concentration fluctuations. From the temperature-dependent behavior of the overall scattering intensities and the dynamic correlation lengths of the fast mode, the critical temperatures and the scaling exponents are determined. The latter are significantly lower than the static values predicted by mean-field theory, which may be related to the presence of the large-scale inhomogeneities. The effect of the cosolvent methanol on the dynamics is investigated for polymer solutions having c = 30 g L-1 and methanol volume fractions in the solvent mixtures of up to 60 vol %. The phase diagram was established by differential scanning calorimetry. The slow mode detected by DLS becomes significantly weaker as methanol is added, i.e., the solutions become more homogeneous. Beyond the minimum of the coexistence line, which is located at 40-50 vol % of methanol, the dynamics is qualitatively different from the one at lower methanol contents. Thus, going from the water-rich to the methanol-rich side of the miscibility gap, the change of interaction of the PNIPMAM chains with the two solvents has a severe effect on the collective dynamics.

Mean-Field Ring Polymer Rates Using a Population Dividing Surface.

Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

Half-metallic ferromagneticWeyl fermions related to dynamic correlations in the zinc-blende compound VAs

Abstract The realization of 100% polarized topological Weyl fermions in halfmetallic ferromagnets is of particular importance for fundamental research and spintronic applications. Here, we theoretically investigate the electronic and topological properties of the zinc-blende compound VAs, which was deemed as a halfmetallic ferromagnet related to dynamic correlations. Based on the combination of density functional theory and dynamical mean field theory, we uncover that the halfmetallic ferromagnet VAs exhibit attractive Weyl semimetallic behaviors which are very close to the Fermi level in the DFT + U regime with effect U values ranging from 1.5 eV to 2.5 eV. Meanwhile, we also investigate the magnetization-dependent topological properties; the results show that the change of magnetization directions only slightly affects the positions of Weyl points, which is attributed to the weak spin-orbital coupling effects. The topological surface states of VAs projected on semiinfinite (001) and (111) surfaces are investigated. The Fermi arcs of all Weyl points are clearly visible on the projected Fermi surfaces. Our findings suggest that VAs is a fully spin-polarized Weyl semimetal with many-body correlated effects in the effective U values range from 1.5 to 2.5 eV.

Entanglement and correlations in an exactly-solvable model of a Bose–Einstein condensate in a cavity

An exactly solvable model of a trapped interacting Bose–Einstein condensate (BEC) coupled in the dipole approximation to a quantized light mode in a cavity is presented. The model can be seen as a generalization of the harmonic-interaction model for a trapped BEC coupled to a bosonic bath. After obtaining the ground-state energy and wavefunction in closed form, we focus on computing the correlations in the system. The reduced one-particle density matrices of the bosons and the cavity are constructed and diagonalized analytically, and the von Neumann entanglement entropy of the BEC and the cavity is also expressed explicitly as a function of the number and mass of the bosons, frequencies of the trap and cavity, and the cavity-boson coupling strength. The results allow one to study the impact of the cavity on the bosons and vice versa on an equal footing. As an application we investigate a specific case of basic interest for itself, namely, non-interacting bosons in a cavity. We find that both the bosons and the cavity develop correlations in a complementary manner while increasing the coupling between them. Whereas the cavity wavepacket broadens in Fock space, the BEC density saturates in real space. On the other hand, while the cavity depletion saturates, and hence does the BEC-cavity entanglement entropy, the BEC becomes strongly correlated and eventually increasingly fragmented. The latter phenomenon implies single-trap fragmentation of otherwise ideal bosons, where their induced long-range interaction is mediated by the cavity. Finally, as a complimentary investigation, the mean-field equations for the BEC-cavity system are solved analytically as well, and the breakdown of mean-field theory for the cavity and the bosons with increasing coupling is discussed. Further applications are envisaged.

(Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst^{++}++ [Phys. Rev. A 108, 013323 (2023)]

Large-scale semi-organized rolls in a sheared convective turbulence: Mean-field simulations

Based on a mean-field theory of a non-rotating turbulent convection [T. Elperin et al., Phys. Rev. E 66, 066305, (2002)], we perform mean-field simulations (MFS) of sheared convection that takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. This effect is caused by the production of additional essentially anisotropic velocity fluctuations generated by tangling of the mean-velocity gradients by small-scale turbulent motions due to the influence of the inertial forces during the lifetime of turbulent eddies. These anisotropic velocity fluctuations contribute to the turbulent heat flux. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The lifetimes and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from a two-layer vertical structure with two rolls in the vertical direction before the system reaches steady-state to a one-layer vertical structure with one roll after the system reaches steady state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding the origin of large-scale rolls observed in atmospheric convective boundary layers, as well as in numerical simulations and laboratory experiments.

Out of time order correlation of the Hubbard model with random local disorder.

The out-of-time-order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory and coherent potential approximation combined with diagrammatic perturbation on the Schwinger-Keldysh contour to calculate the OTOC for correlated fermionic systems subjected to both random disorder and electron interaction. Our key finding is that random disorder enhances the OTOC decay in the Hubbard model for the metallic phase in the weakly interacting limit. However, the current limitation of our perturbative solver restricts the applicability to weak interaction regimes.

Effect of Rare-Earth Element Substitution in Superconducting R3Ni2O7 under Pressure

Abstract Recently, high temperature (T c ≈ 80 K) superconductivity (SC) has been discovered in La3Ni2O7 (LNO) under pressure. This raises the question of whether the superconducting transition temperature T c could be further enhanced under suitable conditions. One possible route for achieving higher T c is element substitution. Similar SC could appear in the Fmmm phase of rare-earth (RE) R3Ni2O7 (RNO, R = RE element) material series under suitable pressure. The electronic properties in the RNO materials are dominated by the Ni 3d orbitals in the bilayer NiO2 plane. In the strong coupling limit, the SC could be fully characterized by a bilayer single 3d x 2–y 2 -orbital t–J ∥–J ⊥ model. With RE element substitution from La to other RE element, the lattice constant of the Fmmm RNO material decreases, and the resultant electronic hopping integral increases, leading to stronger superexchanges between the 3d x 2–y 2 orbitals. Based on the slave-boson mean-field theory, we explore the pairing nature and the evolution of T c in RNO materials under pressure. Consequently, it is found that the element substitution does not alter the pairing nature, i.e., the inter-layer s-wave pairing is always favored in the superconducting RNO under pressure. However, the T c increases from La to Sm, and a nearly doubled T c could be realized in SmNO under pressure. This work provides evidence for possible higher T c R3Ni2O7 materials, which may be realized in further experiments.

Assessment of effective electrical conductivity in spherocylindrical carbon nanotube composites incorporating intrinsic properties of CNTs and interphase layer

This study introduces an analytical model using mean-field theory to estimate the effective electrical conductivity in composites of spherocylindrical carbon nanotubes (CNTs). The model adjusts the interphase layer's thickness and conductivity based on CNT concentration, affecting the electrical tunneling effect, and incorporates the properties of both CNTs and the interphase layer. Validated through detailed comparisons with experimental data, the model accurately predicts the electrical conductivities of polymer-CNT composites (PCNTs). Mean Squared Error analysis highlights its enhanced precision and superiority over traditional cylindrical CNT models. The model also explores how CNT dimensions, intrinsic conductivity, tunneling distance, potential barrier height, and variations in interphase thickness and conductivity influence electrical conductivity and percolation thresholds. This analytical model improves accuracy in predicting PCNT electrical conductivity and provides critical insights for designing and optimizing conductive polymer nanocomposites.

Statistical modeling of equilibrium phase transition in confined fluids

The phase transition of confined fluids in mesoporous materials deviates from that of bulk fluids due to the interactions with the surrounding heterogeneous structure. For example, adsorbed fluids in metal-organic-frameworks (MOFs) have atypical phase characteristics such as capillary condensation and higher-order phase transitions due to a strong heterogeneous field. Considering a many-body problem in the presence of a nonuniform external field, we model the host-guest and guest-guest interactions in MOFs. To solve the three-dimensional Ising model, we use the mean-field theory to approximate the guest-guest interactions and Mayer's f-functions to describe the host-guest interactions in a unit cell. Later, using Hill's theory of nanothermodynamics, we define differential thermodynamic functions to understand the distribution of intensive properties and integral thermodynamic functions to explain the phase transition in confined fluids. The investigation reveals a distinct behavior where fluids confined in larger pores undergo a discontinuous (first-order) phase transition, whereas those confined in smaller pores experience a continuous (higher-order) phase transition. Furthermore, it is observed that the free-energy barrier for low-density adsorbed fluid (LDAF) to high-density adsorbed fluid (HDAF) phase transitions is lower in confined fluids than in bulk fluids resulting in a lower condensation pressure relative to the bulk saturation pressure. Finally, the integral thermodynamic functions are succinctly presented in the form of a phase diagram, marking an initial step toward a more practical approach for understanding the phase behavior of confined fluids. Published by the American Physical Society 2024

Dynamical analysis of the low-temperature phase diagram of a cuprate superconductor

For a cuprate superconductor, specifically the yttrium barium copper oxide system, we analyze the low-temperature phase diagram consisting of the superconducting, pseudogap, and normal phases by using a phonon-mediated attraction and Coulomb repulsion mechanism. Through this analysis, we show this mechanism in the cuprate is quite important for its key dynamics. For the pairing mechanism, a variational method is developed and applied, and a generalized mean field theory is used to calculate the condensate energy and the energy gap of the quasiparticle. We obtain a self-consistent system of equations for these quantities. The superconducting and pseudogap phases, which involve pair-condensates, are assumed to be equilibrium systems of the condensate and normal subphases. The condition for the phase transition point is given by the equal total electronic energy gains. Assuming that the difference in the pairing range of the pair condensate is small between just above and below the transition temperature, computations are performed to solve the self-consistent system of equations. We find solutions compatible with experimental data. Plausible values of the energy gap in the superconducting phase and in the pseudogap phase are obtained. The present analysis shows that the phonon-mediated attraction and Coulomb repulsion mechanism itself is compatible with the experimental data. The importance of the screening effect through one-phonon exchange in the pairing mechanism and of the structure of the valence band is discussed.