Self-energy Function Research Articles

Interface modeling analysis using density functional theory in highly reliable Pt/HfO2/TaOx/Ta self-rectifying memristor

The self-rectifying memristor (SRM) is a promising device prototype for high-density three-dimensional (3D) integration and high-efficiency in-memory computing (IMC) by virtue of its ability to effectively suppress sneak current, simple device structure, and low energy consumption. Theoretically understanding the intrinsic mechanisms of SRM is a matter of concern. Here, we fabricated a Ta/TaOx/HfO2/Pt-stacked SRM exhibiting >103 on/off ratio, rectification ratio, and nonlinearity. The SRM can be repeatedly programmed by more than 106 pulses and demonstrates robust retention and high scalability (∼59 Mbit). A reasonable interface model for this SRM is established based on first-principles calculations. Using self-energy corrected density function theory, we calculate the barrier heights at each interface. Detailed I–V curve fitting and energy band analysis are performed and computationally verified to explain the intrinsic reasons for resistive switching, self-rectifying, and nonlinear behaviors. The work may advance the development of SRM prototype to enable energy-efficient 3D IMC.

Effect of thermal fluctuations on the nontrivial topology of thed + idsuperconducting phase.

The behavior of the topological index (TI), characterizing the properties of superconducting phases of quasi-two-dimensional systems with nontrivial topology, is investigated depending on the temperature and system parameters. For this purpose, a method of calculating the TI, based on a self-consistent functional-integral theory, is proposed. The chirald + idsuperconducting phase of a quasi-two-dimensional model with effective attraction between the electrons located at the nearest sites of a triangular lattice is considered. It is shown that the structure of the energy dependence of the self-energy function, which occurs when taking into account thermal fluctuations, does not lead to a change in the topological properties of the system. It is found that taking into account thermal fluctuations with an increase in the effective attraction between electrons expands the temperature range in which the value of the TI is close to the integerC1≃-2.

Fermion self-energy and damping rate in a hot magnetized plasma

We derive a general expression for the fermion self-energy in a hot magnetized plasma by using the Landau-level representation. In the one-loop approximation, the Dirac structure of the self-energy is characterized by five different functions that depend on the Landau-level index n and the longitudinal momentum pz. We derive general expressions for all five functions and obtain closed-form expressions for their imaginary parts. The latter receive contributions from three types of on shell processes, which are interpreted in terms of Landau-level transitions, accompanied by a single photon (gluon) emission or absorption. By making use of the imaginary parts of the self-energy functions, we also derive the Landau-level dependent fermion damping rates Γn(pz) and study them numerically in a wide range of model parameters. We also demonstrate that the two-spin degeneracy of the Landau levels is lifted by the one-loop self-energy corrections. While the spin splitting of the damping rates is small, it may be important for some spin and chiral effects. We argue that the general method and the numerical results for the rates can have interesting applications in heavy-ion physics, astrophysics, and cosmology, where strongly magnetized QED or QCD plasmas are ubiquitous. Published by the American Physical Society 2024

Origin of minimal conductivity in Dirac materials: Momentum-dependent self-energy function from long-ranged disorder scattering

Origin of minimal conductivity in Dirac materials: Momentum-dependent self-energy function from long-ranged disorder scattering

ACFlow: An open source toolkit for analytic continuation of quantum Monte Carlo data

The purpose of analytic continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, spin and charge susceptibilities) from noisy data generated in finite temperature quantum Monte Carlo simulations. It requires numerical solutions of a family of Fredholm integral equations of the first kind, which is indeed a challenging task. In this paper, an open source toolkit (dubbed ACFlow) for analytic continuation of quantum Monte Carlo data is presented. We first give a short introduction to the analytic continuation problem. Next, three popular analytic continuation algorithms, including the maximum entropy method, the stochastic analytic continuation, and the stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate on the major features, implementation details, basic usage, inputs, and outputs of this toolkit. Finally, four representative examples, including analytic continuations of Matsubara self-energy function, Matsubara and imaginary time Green's functions, and current-current correlation function, are shown to demonstrate the usefulness and flexibility of the ACFlow toolkit. Program summaryProgram Title: ACFlowCPC Library link to program files:https://doi.org/10.17632/th6w74gwjm.1Developer's repository link:https://github.com/huangli712/ACFlowLicensing provisions: GNU General Public License Version 3Programming language: JuliaNature of problem: Most of the quantum Monte Carlo methods work on imaginary axis. In order to extract physical observables and compare them with the experimental results, analytic continuation must be done in the post-processing stage to convert the quantum Monte Carlo simulated data from imaginary axis to real axis.Solution method: Three well-established analytic continuation methods, including the maximum entropy method, the stochastic analytic continuation (both A. W. Sandvik's and K. S. D. Beach's algorithms), and the stochastic optimization method, have been implemented in the ACFlow toolkit.Additional comments including restrictions and unusual features: The ACFlow toolkit is written in pure Julia language. It is highly optimized and parallelized. It can be executed interactively in a Jupyter notebook environment.

Efficient full frequency GW for metals using a multipole approach for the dielectric screening

The properties of metallic systems with important and structured excitations at low energies, such as Cu, are challenging to describe with simple models like the plasmon pole approximation (PPA), and more accurate and sometimes prohibitive full frequency approaches are usually required. In this paper we propose a numerical approach to $GW$ calculations on metals that takes into account the frequency dependence of the screening via the multipole approximation (MPA), an accurate and efficient alternative to current full-frequency methods that was recently developed and validated for semiconductors and overcomes several limitations of PPA. We now demonstrate that MPA can be successfully extended to metallic systems by optimizing the frequency sampling for this class of materials and introducing a simple method to include the $\mathbf{q}\to 0$ limit of the intra-band contributions. The good agreement between MPA and full frequency results for the calculations of quasi-particle energies, polarizability, self-energy and spectral functions in different metallic systems confirms the accuracy and computational efficiency of the method. Finally, we discuss the physical interpretation of the MPA poles through a comparison with experimental electron energy loss spectra for Cu.

Renormalization in Quantum Brain Dynamics

We show renormalization in Quantum Brain Dynamics (QBD) in 3+1 dimensions, namely Quantum Electrodynamics with water rotational dipole fields. First, we introduce the Lagrangian density for QBD involving terms of water rotational dipole fields, photon fields and their interactions. Next, we show Feynman diagrams with 1-loop self-energy and vertex function in dipole coupling expansion in QBD. The counter-terms are derived from the coupling expansion of the water dipole moment. Our approach will be applied to numerical simulations of Kadanoff–Baym equations for water dipoles and photons to describe the breakdown of the rotational symmetry of dipoles, namely memory formation processes. It will also be extended to the renormalization group method for QBD with running parameters in multi-scales.

Hadronic vacuum polarization and the MUonE proposal

The MUonE proposal at the CERN SPS consists in extracting the value of the hadronic vacuum polarization self-energy function (HVP) from its contribution to the differential cross-section of elastic muon-electron scattering. The HVP contribution to the muon anomalous magnetic moment can then be obtained from a weighted integral of the measured HVP self-energy function. This, however, requires a knowledge of the HVP function in its full integration domain. This paper discusses a procedure to reconstruct the HVP function in the regions not directly accessible to measurement. The method is based on the so-called transfer theorems, due to Flajolet and Odlyzko, which we explain and adapt to HVP.

Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model

We investigate several fundamental characteristics of the multiloop functional renormalization group (mfRG) flow by hands of its application to a prototypical many-electron system: the Anderson impurity model (AIM). We first analyze the convergence of the algorithm in the different parameter regions of the AIM. As no additional approximation is made, the multiloop series for the local self-energy and response functions converge perfectly to the corresponding results of the parquet approximation (PA) in the weak- to intermediate-coupling regime. Small oscillations of the mfRG solution as a function of the loop order gradually increase with the interaction, hindering a full convergence to the PA in the strong-coupling regime, where perturbative resummation schemes are no longer reliable. By exploiting the converged results, we inspect the fulfillment of (i) sum rules associated to the Pauli principle and (ii) Ward identities related to conservation laws. For the Pauli principle, we observe a systematic improvement by increasing the loop order and including the multiloop corrections to the self-energy. This is consistent with the preservation of crossing symmetries and two-particle self-consistency in the PA. For the Ward identities, we numerically confirm a visible improvement by means of the Katanin substitution. At weak coupling, violations of the Ward identity are further reduced by increasing the loop order in mfRG. In this regime, we also determine the precise scaling of the deviations of the Ward identity as a function of the electronic interaction. For larger interaction values, the overall behavior becomes more complex, and the benefits of the higher-loop terms are mostly present in the contributions at large frequencies.

Quasiparticle multiplets and 5f electronic correlation in prototypical plutonium borides

In this paper, we investigate the electronic structures of plutonium borides (PuB x , x = 1, 2, 6, 12) to uncover the fascinating bonding behavior and orbital dependent correlations of 5f valence electrons by using the density functional theory combined with single-site dynamical mean-field method. We not only reproduce the correlated topological insulator of PuB6, but also predict the metallicity in PuB x (x = 1, 2, 12). It is found that the band structure, density of states, hybridization functions all indicate partially itinerant 5f states in PuB x (x = 1, 2, 6, 12). Especially, quasiparticle multiplets induced noteworthy valence state fluctuations implying the mixed-valence behavior of plutonium borides. Moreover, the itinerant degree of freedom for 5f electrons in PuB x (x = 1, 2, 12) is tuned by hybridization strength between 5f states and conduction bands, which is affected by atomic distance in plutonium borides. Lastly, 5f electronic correlations encoded in the electron self-energy functions demonstrate moderate 5f electronic correlations in PuB6 and orbital selective 5f electronic correlations in PuB x (x = 1, 2, 12). Consequently, the understanding of electronic structure and related crystal structure stability shall shed light on exploring novel 5f electrons states and ongoing experiment study.

Single particle properties of the two-dimensional Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions

We generate the perturbative expansion of the single particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle quantities for real and Matsubara frequencies and verify results through comparison to existing data on the Matsubara axis. With low-order expansions at weak coupling we observe a number of outcomes expected at higher orders: the opening of a gap, pseudogap behavior, and Fermi-surface reconstruction. Based on low-order perturbations, we consider the phase diagram that arises from truncated expansions of the self-energy and Green's function and their relation via the Dyson equation. From Matsubara axis data, we observe insulating behavior in direct expansions of the Green's function, whereas the same order of truncation of the self-energy produces metallic behavior. This observation is supported by additional calculations for real frequencies. We attribute this difference to the order in which diagrams are implicitly summed in the Dyson series. By separating the reducible and irreducible contributions at each order we show that the reducible diagrams implicitly summed in the Dyson equation lead to incorrect physics in the half-filled Hubbard model. Our observations for this particular case lead us to question the utility of the Dyson equation for any problem that shows a disparity between reducible and irreducible contributions to the expansion of the Green's function.

Strong interaction of a quantum dot with the photon reservoir in one-dimensional photonic crystals

Quantum fluctuations as a process of the self-interaction of a system lead to a shift of the energy levels and are usually described by the self-energy function. Here quantum fluctuations caused by the interaction of a quantum dot coupled with an one-dimensional photonic crystal’s cavity with the photon reservoir are discussed. It is shown that this interaction can lead to a significant increase in quantum fluctuations. The self-interaction is of interest for solving problems of decreasing decoherence and dephasing of qubit for quantum computation.

Nonperturbative renormalization of the interaction of quantum dots with the phonon reservoir

The quantum dynamics of a single quantum dot with phonon reservoir is investigated by making use generalized quantum dynamics equation [Gainutdinov R.Kh. 1999 J. Phys. A 32 5675]. The self-energy function is calculated nonperturbatively taking into account the renormalization of the vertex function. In this paper, we show that the nonperturbative renormalization of the vertex function significantly affects the nature of the interaction of the quantum dot with the phonon reservoir.

Unraveling the 4f electronic structures of cerium monopnictides

We employed a state-of-the-art first-principles many-body approach, namely the density functional theory in combination with the single-site dynamical mean-field theory, to study the 4f electronic structures in cerium monopnictides (CeX, where X = N, P, As, Sb, and Bi). We find that the 4f electrons in CeN are highly itinerant and mixed-valence, showing a prominent quasiparticle peak near the Fermi level. On the contrary, they become well localized and display weak valence fluctuation in CeBi. It means that a 4f itinerant-localized crossover could emerge upon changing the X atom from N to Bi. Moreover, according to the low-energy behaviors of 4f self-energy functions, we could conclude that the 4f electrons in CeX also demonstrate interesting orbital-selective electronic correlations, which are similar to the other cerium-based heavy fermion compounds.

Mass dimension one fermions at 1-loop

We investigate 1-loop contributions to the 2- and 4-point correlation functions within a theory for fermions with mass dimension one with a simple quartic self-interaction term. The 1-loop divergence appearing the self-energy function can be consistently absorbed by renormalization of the mass parameter. In the case of the (1PI) 4-point correlation function, there is a surprising cancellation of divergences coming from different diagrams, leading to a finite 1-loop result. The inclusion of a complete basis of four-fermion interactions is discussed.

Nonperturbative Effects in the Emission Spectra of Quantum Dots Interacting with Bosonic and Fermionic Reservoirs

The problem of the description of the strong interaction of the InAs/GaAs exciton quantum dot (QD) grown by molecular-beam epitaxy with acoustic phonon and electron reservoirs is studied. A nonperturbative solution to the self-energy function of the exciton quantum dot is found. It is shown that these functions at temperatures higher than 10 K differ significantly from those obtained within in the Born approximation. The accurate calculation of the self-energy function of the exciton QD makes it possible to solve the problem of decoherence and dephasing of quantum states, which opens the way to develop single-photon sources necessary in quantum calculations and quantum communication.

Exploring the exotic f states of prototype compounds CeSb and USb

To unravel the interplay between the strong electronic correlation and itinerant-localized dual nature in typical f electron systems, we employed the density functional theory in combination with the single-site dynamical mean-field theory to systematically investigate the electronic structures of CeSb and USb. We find that the 4f states in CeSb are mostly localized with a weak quasi-particle resonance peak near the Fermi level. Conversely, the 5f electrons in USb display partially itinerant features, accompanied by mixed-valence behavior and prominent valence state fluctuations. Particularly, the 4f electronic correlations in CeSb are orbital-selective with strikingly renormalized 4f5/2 states, according to the low-energy behaviors of 4f self-energy functions. It is believed that the strong electronic correlation and fantastic bonding of f states contribute to elucidating the magnetism.

Nature of the 5f electronic structure of plutonium

Plutonium (Pu), in which the 5$f$ valence electrons always wander the boundary between localized and itinerant states, exhibits quite complex crystal structures and unprecedentedly anomalous properties with respect to temperature and alloying. Understanding its chemical and physical properties, especially its 5$f$ electronic structure is one of the central and unsolved topics in condensed matter theory. In the present work, the electronic structures of the six allotropes of Pu (including its $\alpha$, $\beta$, $\gamma$, $\delta$, $\delta'$, and $\epsilon$ phases) at ambient pressure are studied comprehensively by means of the density functional theory in combination with the single-site dynamical mean-field theory. The band structures, total and partial density of states, valence state histograms, 5$f$ orbital occupancies, X-ray branching ratios, and self-energy functions are carefully studied. It is suggested that the $\alpha$, $\beta$, and $\gamma$ phases of Pu are typical Racah metals in which the atomic multiple effect dominates near the Fermi level. The calculated results reveal that not only the $\delta$ phase, but also all the six allotropes are archetypal mixed-valence metals with remarkable atomic eigenstate fluctuation. In consequence of that, the 5$f$ occupancy $n_{5f}$ is around 5.1 $\sim$ 5.4, which varies with respect to the atomic volume and electronic correlation strength of Pu. The 5$f$ electronic correlation in Pu is moderately orbital-dependent. Moreover, the 5$f$ electrons in the $\delta'$ phase are the most correlated and localized.

Pairing and non-Fermi liquid behavior in partially flat-band systems: Beyond nesting physics

While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems.

Coupled Cluster as an Impurity Solver for Green's Function Embedding Methods.

We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on the non-Hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled one-dimensional (1D) Hubbard model projected onto a single-site impurity problem and a half-filled two-dimensional (2D) Hubbard model projected onto a four-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of Green's function CCSD solver within the Self-Energy Embedding Theory (SEET) with Hartree-Fock (HF) and Green's Function second order (GF2) for the treatment of the environment.