Dynamical Mean-field Theory Research Articles

Prediction of anomalies in the velocity of sound for the pseudogap of hole-doped cuprates

We predict sound anomalies at the doping $\delta_{p}$ where the pseudogap ends in the normal state of hole-doped cuprates. Our prediction is based on the two-dimensional compressible Hubbard model using cluster dynamical mean-field theory. We find sharp anomalies (dips) in the velocity of sound as a function of doping and interaction. These dips are a signature of supercritical phenomena, stemming from an electronic transition without symmetry breaking below the superconducting dome. If experimentally verified, these signatures may help to solve the fundamental question of the nature of the pseudogap -- pinpointing its origin as due to Mott physics and resulting short-range correlations.

Dynamical mean-field study of a photon-mediated ferroelectric phase transition

The interplay of light and matter gives rise to intriguing cooperative effects in quantum many-body systems. This is even true in thermal equilibrium, where the electromagnetic field can hybridize with collective modes of matter, and virtual photons can induce interactions in the solid. Here, we show how these light-mediated interactions can be treated using the dynamical mean-field theory formalism. We consider a minimal model of a two-dimensional material that couples to a surface plasmon polariton mode of a metal-dielectric interface. Within the mean-field approximation, the system exhibits a ferroelectric phase transition that is unaffected by the light-matter coupling. Bosonic dynamical mean-field theory provides a more accurate description and reveals that the photon-mediated interactions enhance the ferroelectric order and stabilize the ferroelectric phase.

Thermal conductivity and heat diffusion in the two-dimensional Hubbard model

We study the electronic thermal conductivity $\kappa_\textrm{el}$ and the thermal diffusion constant $D_\textrm{Q,el}$ in the square lattice Hubbard model using the finite-temperature Lanczos method. We exploit the Nernst-Einstein relation for thermal transport and interpret the strong non-monotonous temperature dependence of $\kappa_\textrm{el}$ in terms of that of $D_\textrm{Q,el}$ and the electronic specific heat $c_\textrm{el}$. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that $\kappa_\textrm{el}$ is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above or close to lattice spacing. We discuss the opposite effect of quasi-particle renormalization on charge and heat diffusion constants. We calculate the Lorenz ratio and show that it differs from the Sommerfeld value. We discuss our results in relation to experiments on cuprates. Additionally, we calculate the thermal conductivity of overdoped cuprates within the anisotropic marginal Fermi liquid phenomenological approach.

Electron-electron interactions and high-order harmonics in solids

The generation of high-order harmonics in bulk systems is a young and fast-growing area of research. Beginning in 2011 with the pioneering studies of high-order harmonic generation in bulk dielectrics, significant progress has already been made in understanding the details of the microscopic mechanisms behind this phenomenon, such as the role of intra- and interband polarization, the contribution of the electronic band structure and dipole moments to the harmonic spectrum, and the effects of structural and electronic symmetry. However, the role of electron-electron correlations in the excited system is much less understood. In this work, we study the role of these effects in the high-order harmonic spectrum by using the Time-Dependent Density Functional Theory (TDDFT) approach with the Dynamical Mean-Field Theory (DMFT) exchange-correlation kernel. In this approximation, one takes into account the time-resolved on-site electron-electron interactions. As we demonstrate, the correlation effects significantly affect the high-harmonic spectrum, most importantly through ultrafast modification of the interband polarization of the system.

Mixed valence nature of the Ce4fstate inCeCo5based on spin-polarizedDFT+DMFTcalculations

Cerium-based intermetallics are currently attracting much attention as highly promising alternatives to conventional permanent magnets that contain a scarce rare earth element like neodymium. In the present work we apply a charge fully self-consistent approach combining density functional theory and dynamical mean-field theory (DFT $+$ DMFT) to investigate the magnetization and electronic structure of the ${\mathrm{CeCo}}_{5}$ system. We treat simultaneously the correlation effects in Ce-$4f$ and Co-$3d$ orbitals while taking the spin polarization into account. The calculated magnetic moment corresponding to the Ce-$4f$ shell using the DFT $+$ DMFT method is found to be drastically reduced as compared to the DFT results. Moreover, the Ce-$4f$ valence state fluctuations are evaluated and compared within ${\mathrm{CeCo}}_{5}$ and $\mathrm{Ce}{({\mathrm{Co}}_{0.8}{\mathrm{Cu}}_{0.2})}_{5}$ on account of the trivalent Ce in ${\mathrm{CeCu}}_{5}$. Regarding the Cu substitutions at two Wyckoff positions of Co (2c and 3g), the substitution at 3g sites slightly enhances the magnetic moment of Ce while the substitution at 2c sites leads to nearly vanishing Ce and Co moments. Such a contrast may contribute to the experimentally reported nonmonotonic change of the magnetic anisotropy with increasing Cu alloying content in $\mathrm{Ce}{({\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x})}_{5}$ alloys.

Inter-configuration fluctuation for 5f electrons in uranium hexafluoride: A many-body study

A quantum mechanics calculation is performed on uranium hexafluoride (UF6) by using density functional theory (DFT) combing with dynamical mean-field theory (DMFT) scheme, taking into account the spin–orbit coupling (SOC) interaction and the on-site 5f-5f Coulomb repulsion. Results demonstrate that SOC-splitting j = 5/2 and j = 7/2 manifolds are in the metallic and insulating regimes, respectively, albeit both are in weakly correlated states. Ratio of the quasi-particle weights R = Zj=7/2/Zj=5/2 is about 1, suggesting that UF6 is not in the so-called orbital-selective localized state. Russel-Saunders (LS) coupling scheme is feasible for U 5f electrons. U 5f-conduction electrons hybridization, 5f-5f correlation, SOC interaction and final state effects yield a complicated spectrum function. Occupation probability analysis shows that 5f electrons exhibit the so-called inter-configuration fluctuation (ICF) due to admixing of 5f1 and 5f3 atomic configurations into 5f2 configuration with an average occupation number of n5f ∼ 1.8585, mainly arising from the complicated quantum mechanics processes including the dual nature of localized and itinerant 5f electrons, a quantum mechanical mixture of the energetically degenerate 5fn configurations, as well as the flexible outer electronic configuration of U ions. Finally, the momentum-resolved electronic spectrum function (the so-called quasiparticle band structure) is also discussed.

Single- and two-particle finite size effects in interacting lattice systems

Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an efficient strategy to eliminate one-body finite size effects. In the dynamical mean field community, cluster generalizations of the dynamical mean field theory were formulated to study systems with nonlocal correlations. In this work, we put the twist-averaging and the dynamical cluster approximation variant of the dynamical mean field theory onto equal footing, discuss commonalities and differences, and compare results from both techniques to the standard periodic boundary technique. At the example of Hubbard-type models with local, short-range and Yukawa-like longer range interactions we show that all methods converge to the same limit, but that the convergence speed differs in practice. We show that embedding theories are an effective tool for managing both one-body and two-body finite size effects, in particular if interactions are averaged over twist angles.

Input correlations impede suppression of chaos and learning in balanced firing-rate networks.

Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A distinctive feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far more difficult to suppress chaos with common input into each neuron than through independent input. To study this phenomenon, we develop a non-stationary dynamic mean-field theory for driven networks. The theory explains how the activity statistics and the largest Lyapunov exponent depend on the frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We further show that uncorrelated inputs facilitate learning in balanced networks.

Nonequilibrium DMFT+CPA for correlated disordered systems

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.

Effect of local magnetic moments on spectral properties and resistivity near interaction- and doping-induced Mott transitions

We study the effect of the formation and screening of local magnetic moments on the temperature- and interaction dependencies of spectral functions and resistivity in the vicinity of the metal-insulator transition. We use the dynamical mean-field theory for the strongly correlated Hubbard model and associate the peculiarities of the above mentioned properties with those found for the local charge $\chi_c$ and spin $\chi_s$ susceptibilities. We show that at half filling the maximum of resistivity at a certain temperature $T^*$ corresponds to the appearance of central quasiparticle peak of the spectral function and entering the metallic regime with well defined fermionic quasiparticles. At the same time, the temperature of the crossover to the regime with screening of local magnetic moments, determined by the minimum of double occupation, is smaller than the temperature scale $T^*$ and coincides at half filling with the boundary $T_{\beta=1}(U)$ corresponding to the exponent of resistivity $\beta\equiv d\ln \rho/d\ln T=1$. Away from half filling we find weak increase of the temperature of the beginning and completion of the screening (i.e. Kondo temperature) of local magnetic moments, while the unscreened local magnetic moments exist only up to few percents of doping. In the low temperature regime $T<T_{\beta=1}$ simultaneous presence of itinerant and localized degrees of freedom yields almost linear temperature dependence of scattering rate and resistivity.

Dynamical mean-field theory: from ecosystems to reaction networks

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species’ abundances, albeit at vastly different scales. The maintenance of diversity in large ecosystems is a longstanding puzzle, towards which recent progress has been made by the derivation of dynamical mean-field theories of random models. In particular, it has recently been shown that these random models have a chaotic phase in which abundances display wild fluctuations. When modest spatial structure is included, these fluctuations are stabilized and diversity is maintained. If and how these phenomena have parallels in biochemical reaction networks is currently unknown. Making this connection is of interest since life requires cooperation among a large number of molecular species. In this work, we find a reaction network whose large-scale behavior recovers the random Lotka–Volterra model recently considered in theoretical ecology. We clarify the assumptions necessary to derive its large-scale description, and reveal the underlying assumptions made on the noise to recover previous dynamical mean-field theories. Then, we show how local detailed balance and the positivity of reaction rates, which are key physical requirements of chemical reaction networks, provide obstructions towards the construction of an associated dynamical mean-field theory of biochemical reaction networks. Finally, we outline prospects and challenges for the future.

Local electron correlation effects on the fermiology of the weak itinerant ferromagnet ZrZn2

The Fermi surface topology plays an important role in the macroscopic properties of metals. It can be particularly sensitive to electron correlation, which appears to be especially significant for the weak itinerant ferromagnet ZrZn2. Here, we look at the differences in the predicted Fermi surface sheets of this metallic compound in its paramagnetic phase for both density functional theory (DFT) and the combination of DFT with dynamical mean field theory (DFT + DMFT). The theoretical spectral functions evaluated at the Fermi level were used along with calculations of the electron–positron momentum density (also known as the two-photon momentum density) in k-space to provide insights into the origin of certain features of the Fermi surface topology. We compare this two photon momentum density to that extracted from the positron annihilation experimental data (2004 Phys. Rev. Lett. 92 107003). The DFT + DMFT densities are in better agreement with the experiment than the DFT, particularly with regard to the flat bands around the L and W high symmetry points. The experimental neck around L, which relates to a van Hove singularity, is present in DFT + DMFT but not in the DFT. We find that these flat bands, and as such the Fermi surface topology, are sensitive to the many body electron correlation description, and show that the positron annihilation technique is able to probe this. This description is significant for the observed behavior such as the Lifshiftz transition around the quantum critical point.

Satellites in the Ti 1s core level spectra of SrTiO3 and TiO2

Satellites in core level spectra of photoelectron spectroscopy (PES) can provide crucial information on the electronic structure and chemical bonding in materials, particular in transition metal oxides. This paper explores satellites of the Ti 1$s$ and 2$p$ core level spectra of SrTiO$_3$ and TiO$_2$. Conventionally, soft x-ray PES (SXPS) probes the Ti 2$p$ core level; however, it is not ideal to fully capture satellite features due to its inherent spin-orbit-splitting (SOS). Here, hard x-ray PES(HAXPES) provides access to the Ti 1$s$ spectrum instead, which allows us to study intrinsic charge responses upon core-hole creation without the complication from SOS and with favorable intrinsic linewidths. The experimental spectra are theoretically analyzed by two impurity models, including an Anderson impurity model (AIM) built on local density approximation (LDA) and dynamical mean-field theory (DMFT), and a conventional TiO$_6$ cluster model. The theoretical results emphasize the importance of explicit inclusion of higher-order Ti-O charge-transfer processes beyond the nearest-neighboring Ti-O bond to simulate the core level spectra of SrTiO$_3$ and TiO$_2$. The AIM approach with continuous bath orbitals provided by LDA+DMFT represents the experimental spectra well. Crucially, with the aid of the LDA+DMFT method, this paper provides a robust prescription of how to use the computationally cheap cluster model in fitting analyses of core level spectra.

Model for the dynamics of carrier injection in a band with polaronic states: Application to exciton dissociation in organic solar cells

We develop a quantum model for the dynamics of carrier injection in a band that presents a strong carrier-vibration coupling. This coupling modifies the spectral density of the band and can even create pseudogaps that signal the onset of polaronic states. The injection of a carrier that interacts with many vibration modes is a complex many-body process that is treated by combining the quantum scattering theory and the dynamical mean-field theory (DMFT). For the model analyzed here, which is adapted to compact phases, the number $Z$ of neighbors of a given site is large and in this limit the DMFT becomes exact. The model is applied to the excitonic dissociation at the donor-acceptor interface for organic solar cells. The main ingredients are the electron-hole Coulomb interaction, the recombination process, and the existence of polaronic states in the acceptor band. Using parameters extracted from ab initio calculations we analyze the spectral density on the charge transfer state (CTS), the average energy transferred to phonons on the CTS, and the quantum yield of the injection process. We find in particular that even with a strong electron-vibration coupling, one can get a vibrationally cold charge transfer state with a high injection yield as often observed experimentally.

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting ${T}_{c}$. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the interlayer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting---and to reach the largest order parameter---in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity.

Impact ionization processes in a photodriven Mott insulator: Influence of phononic dissipation

We study a model for photovoltaic energy collection consisting of a Mott insulating layer in presence of acoustic phonons, coupled to two wide-band fermion leads at different chemical potentials and driven into a nonequilibrium steady state by a periodic electric field. We treat electron correlations with nonequilibrium dynamical mean-field theory (DMFT) using the so-called auxiliary master equation approach as impurity solver and include dissipation by acoustic phonons via the Migdal approximation. For a small hybridization to the leads, we obtain a peak in the photocurrent as a function of the driving frequency which can be associated with impact ionization processes. For larger hybridizations the shallow peak suggests a suppression of impact ionization with respect to direct photovoltaic excitations. Acoustic phonons slightly enhance the photocurrent for small driving frequencies and suppress it at frequencies around the main peak at all considered hybridization strengths.

Precise ground state of multiorbital Mott systems via the variational discrete action theory

Determining the ground state of multi-orbital Hubbard models is critical for understanding strongly correlated electron materials, yet existing methods struggle to simultaneously reach zero temperature and infinite system size. The \textit{de facto} standard is to approximate a finite dimension multi-orbital Hubbard model with a $d=\infty$ version, which can then be formally solved via the dynamical mean-field theory (DMFT), though the DMFT solution is limited by the state of unbiased impurity solvers for zero temperature and multiple orbitals. The recently developed variational discrete action theory (VDAT) offers a new approach to solve the $d=\infty$ Hubbard model, with a variational ansatz that is controlled by an integer $\mathcal{N}$, and monotonically approaches the exact solution at an increasing computational cost. Here we propose a decoupled minimization algorithm to implement VDAT for the multi-orbital Hubbard model in $d=\infty$ and study $\mathcal{N}=2-4$ . At $\mathcal{N}=2$, VDAT rigorously recovers the multi-orbital Gutzwiller approximation, reproducing known results. At $\mathcal{N}=3$, VDAT precisely captures the competition between the Hubbard $U$, Hund $J$, and crystal field $\Delta$ in the two orbital Hubbard model over all parameter space, with a negligible computational cost. For sufficiently large $U/t$ and $J/U$, we show that $\Delta$ drives a first-order transition within the Mott insulating regime. In the large orbital polarization limit with finite $J/U$, we find that interactions have a nontrivial effect even for small $U/t$. VDAT will have far ranging implications for understanding multi-orbital model Hamiltonians and strongly correlated electron materials.

Active orbital degree of freedom and potential spin-orbit-entangled moments in the Kitaev magnet candidate BaCo2(AsO4)2

Candidate materials for Kitaev spin liquid phase have been intensively studied recently because of their potential applications in fault-tolerant quantum computing. Although most of the studies on Kitaev spin liquid have been done in 4$d$ and 5$d$ based transition metal compounds, recently there has been a growing research interest in Co-based quasi-two-dimensional honeycomb magnets, such as BaCo$_2$(AsO$_4$)$_2$ because of formation of spin-orbit-entangled $J_{\rm eff}$ = 1/2 pseudospin moments at Co$^{2+}$ sites and potential realizations of Kitaev-like magnetism therein. Here, we obtain high-accuracy crystal and electronic structure of BaCo$_2$(AsO$_4$)$_2$ by employing a combined density functional and dynamical mean-field theory calculations, which correctly capture the Mott-insulating nature of the target system. We show that Co$^{2+}$ ions form a high spin configuration, $S=3/2$, with an active $L_{\rm eff}=1$ orbital degree of freedom, in the absence of spin-orbit coupling. The size of trigonal distortion within CoO$_6$ octahedra is found to be not strong enough to completely quench the orbital degree of freedom, so that the presence of spin-orbit coupling can give rise to the formation of spin-orbit-entangled moments and the Kitaev exchange interaction. Our finding supports recent studies on potential Kitaev magnetism in this compound and other Co-based layered honeycomb systems.

Pressure-driven change of ground state of Ce3Pd3Bi4 : A DFT+DMFT study

A candidate material for strongly correlated topological materials, ${\mathrm{Ce}}_{3}{\mathrm{Pd}}_{3}{\mathrm{Bi}}_{4}$ has attracted much attention, but its ground state remains controversial. Compared with the typical Kondo insulator ${\mathrm{Ce}}_{3}{\mathrm{Pt}}_{3}{\mathrm{Bi}}_{4}$, two possibilities of ground states are proposed: ${\mathrm{Ce}}_{3}{\mathrm{Pd}}_{3}{\mathrm{Bi}}_{4}$ is either a spin--orbit-driven topological semimetal or a Kondo insulator with less Kondo coupling strength than platinum. Here, we performed density functional theory $(\mathrm{DFT})+\mathrm{dynamical}$ mean field theory (DMFT) calculations on ${\mathrm{Ce}}_{3}{\mathrm{Pd}}_{3}{\mathrm{Bi}}_{4}$ under different pressures to clarify its ground state, as pressure can tune the strength of Kondo coupling without affecting the strength of spin-orbit coupling. We found ${\mathrm{Ce}}_{3}{\mathrm{Pd}}_{3}{\mathrm{Bi}}_{4}$ has a metallic ground state and becomes insulating with increasing pressure at a low temperature. And as the pressure increased to 2 GPa, a hybridization energy gap can be observed at 10 K. As the pressure increased to 5 GPa, the electronic structure of ${\mathrm{Ce}}_{3}{\mathrm{Pd}}_{3}{\mathrm{Bi}}_{4}$ is even similar to that of the Kondo insulator ${\mathrm{Ce}}_{3}{\mathrm{Pt}}_{3}{\mathrm{Bi}}_{4}$ under ambient pressure, and a clear hybridization energy gap $(\ensuremath{\sim}3\phantom{\rule{0.28em}{0ex}}\mathrm{meV})$ appears at 20 K. Our results not only demonstrate that the key factor controlling the different ground states between the two compounds is Kondo physics, rather than spin-orbit coupling, but also confirm that ${\mathrm{Ce}}_{3}{\mathrm{Pd}}_{3}{\mathrm{Bi}}_{4}$ is an ideal material to tuning the ground states by changing the strength of hybridization by pressure.

Simplified approach to the magnetic blue shift of Mott gaps

The antiferromagnetic ordering in Mott insulators upon lowering the temperature is accompanied by a transfer of the single-particle spectral weight to lower energies and a shift of the Mott gap to higher energies (magnetic blue shift, MBS). The MBS is governed by the double exchange and the exchange mechanisms. Both mechanisms enhance the MBS upon increasing the number of orbitals. By performing a polynomial fit to numerical dynamical mean-field theory data we provide an expansion for the MBS in terms of hopping and exchange coupling of a prototype Hubbard-Kondo-Heisenberg model and discuss how the results can be generalized for application to realistic Mott or charge-transfer insulator materials. This allows estimating the MBS of the charge gap in real materials in an extremely simple way avoiding extensive theoretical calculations. The approach is exemplarily applied to $\alpha$-MnTe, NiO, and BiFeO$_3$ and an MBS of about $130$ meV, $360$ meV, and $157$ meV is found, respectively. The values are compared with the previous theoretical calculations and the available experimental data. Our ready-to-use formula for the MBS simplifies the future studies searching for materials with a strong coupling between the antiferromagnetic ordering and the charge excitations, which is paramount to realize a coupled spin-charge coherent dynamics at a femtosecond time scale.