Showing papers on "Random phase approximation published in 2019"

Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene

Abstract: The recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral (d + id mixed with p−ip) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three M points in the Brillouin Zone, and a 2 × 2 pattern in real space. In simple treatments though, this leads to a full gap at fillings ± (1/2 + 1/8), slightly away from half-filling. The selection of spin-singlet or spin triplet orders, both for the IVCW and the superconductor, arise fcase corresponds to the Hundsrom SO(4) symmetry breaking terms. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.

Dynamical structure factor of strongly coupled ions in a dense quantum plasma.

Abstract: The dynamical structure factor (DSF) of strongly coupled ions in dense plasmas with partially and strongly degenerate electrons is investigated. The main focus is on the impact of electronic correlations (nonideality) on the ionic DSF. The latter is computed by carrying out molecular dynamics (MD) simulations with a screened ion-ion interaction potential. The electronic screening is taken into account by invoking the Singwi-Tosi-Land-Sjolander approximation, and it is compared to the MD simulation data obtained considering the electronic screening in the random phase approximation and using the Yukawa potential. We find that electronic correlations lead to lower values of the ion-acoustic mode frequencies and to an extension of the applicability limit with respect to the wave-number of a hydrodynamic description. Moreover, we show that even in the limit of weak electronic coupling, electronic correlations have a nonnegligible impact on the ionic longitudinal sound speed. Additionally, the applicability of the Yukawa potential with an adjustable screening parameter is discussed, which will be of interest, e.g., for the interpretation of experimental results for the ionic DSF of dense plasmas.

Effect of the anomalous magnetic moment of quarks on the phase structure and mesonic properties in the NJL model

Abstract: Employing a field dependent three-momentum cutoff regularization technique, we study the phase structure and mesonic masses using the 2-flavor Nambu–Jona Lasinio model at finite temperature and density in the presence of an arbitrary external magnetic field. This approach is then applied to incorporate the effects of the anomalous magnetic moment (AMM) of quarks on constituent quark mass and thermodynamic observables as a function of temperature/baryonic density. The critical temperature for transition from chiral symmetry broken to the restored phase is observed to decrease with the external magnetic field, which can be classified as inverse magnetic catalysis, while an opposite behavior is realized in the case of a vanishing magnetic moment, implying magnetic catalysis. These essential features are also reflected in the phase diagram. Furthermore, the properties of the low lying scalar and neutral pseudoscalar mesons are also studied in presence of a hot and dense magnetized medium including AMM of the quarks using random phase approximation. For nonzero values of magnetic field, we notice a sudden jump in the mass of the Goldstone mode at and above the Mott transition temperature which is found to decrease substantially with the increase in magnetic field when the AMM of the quarks are taken into consideration.

Finite-Field Approach to Solving the Bethe-Salpeter Equation.

Abstract: We present a method to compute optical spectra and exciton binding energies of molecules and solids based on the solution of the Bethe-Salpeter equation and the calculation of the screened Coulomb interaction in a finite field. The method does not require either the explicit evaluation of dielectric matrices or of virtual electronic states, and can be easily applied without resorting to the random phase approximation. In addition, it utilizes localized orbitals obtained from Bloch states using bisection techniques, thus greatly reducing the complexity of the calculation and enabling the efficient use of hybrid functionals to obtain single particle wave functions. We report exciton binding energies of several molecules and absorption spectra of condensed systems of unprecedented size, including water and ice samples with hundreds of atoms.

Variational generalized Kohn-Sham approach combining the random-phase-approximation and Green's-function methods

Abstract: Author(s): Voora, Vamsee K; Balasubramani, Sree Ganesh; Furche, Filipp | Abstract: A generalized Kohn–Sham (GKS) scheme which variationally minimizes the random phase approximation (RPA) ground state energy with respect to the GKS one-particle density matrix is introduced. We introduce the notion of functional-selfconsistent (FSC) schemes, which vary the one- particle Kohn–Sham (KS) potential entering an explicitly potential-dependent exchange-correlation (XC) energy functional for a given density, and distinguish them from orbital-selfconsistent (OSC) schemes, which vary the density, or the orbitals, density matrix, or KS potential generating the density. It is shown that, for explicitly potential-dependent XC functionals, existing OSC schemes such as the optimized effective potential method violate the Hellmann-Feynman theorem for the density, producing a spurious discrepancy between the KS density and the correct Hellmann-Feynman density for approximate functionals. A functional selfconsistency condition is derived which resolves this discrepancy by requiring the XC energy to be stationary with respect to the KS potential at fixed density. We approximately impose functional selfconsistency by by semicanonical projection (sp) of the PBE KS Hamiltonian. Variational OSC minimization of the resulting GKS-spRPA energy functional leads to a nonlocal correlation potential whose off-diagonal blocks correspond to orbital rotation gradients, while its diagonal blocks are related to the RPA self-energy at real frequency. Quasiparticle GW energies are a first-order perturbative limit of the GKS-spRPA orbital energies; the lowest-order change of the total energy captures the renormalized singles excitation correction to RPA. GKS-spRPA orbital energies are found to approximate ionization potentials and fundamental gaps of atoms and molecules more accurately than semilocal density functional approximations (SL DFAs) or G0W0 and correct the spurious behavior of SL DFAs for negative ions. GKS-spRPA energy differences are uniformly more accurate than the SL-RPA ones; improvements are modest for covalent bonds but substantial for weakly bound systems. GKS-spRPA energy minimization also removes the spurious maximum in the SL-RPA potential energy curve of Be 2 , and produces a single Coulson-Fischer point at ∼ 2.7 times the equilibrium bond length in H 2 . GKS-spRPA thus corrects most density-driven errors of SL-RPA, enhances the accuracy of RPA energy differences for electron-pair conserving processes, and provides an intuitive one-electron GKS picture yielding ionization potentials energies and gaps of GW quality.

Computing RPA Adsorption Enthalpies by Machine Learning Thermodynamic Perturbation Theory.

Abstract: Correlated quantum-chemical methods for condensed matter systems, such as the random phase approximation (RPA), hold the promise of reaching a level of accuracy much higher than that of conventiona...

Gaussian time-dependent variational principle for the Bose-Hubbard model

Abstract: We systematically extend Bogoliubov theory beyond the mean-field approximation of the Bose-Hubbard model in the superfluid phase. Our approach is based on the time-dependent variational principle applied to the family of all Gaussian states (i.e., Gaussian TDVP). First, we find the best ground-state approximation within our variational class using imaginary time evolution in 1D, 2D, and 3D. We benchmark our results by comparing to Bogoliubov theory and DMRG in 1D. Second, we compute the approximate one- and two-particle excitation spectrum as eigenvalues of the linearized projected equations of motion (linearized TDVP). We find the gapless Goldstone mode, a continuum of two-particle excitations and a doublon mode. We discuss the relation of the gap between Goldstone mode and two-particle continuum to the excitation energy of the Higgs mode. Third, we compute linear response functions for perturbations describing density variation and lattice modulation and discuss their relations to experiment. Our methods can be applied to any perturbations that are linear or quadratic in creation/annihilation operators. Finally, we provide a comprehensive overview how our results are related to well-known methods, such as traditional Bogoliubov theory and random phase approximation.

Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases.

Abstract: We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors. At zero temperature, we analytically continue the equation on the collective mode energy in Anderson's Random Phase Approximation or Gaussian fluctuations through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. The branch exists as long as the chemical potential μ is positive and the wave number below sqrt[2mμ]/ℏ (with m the fermion mass). In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically for an arbitrary interaction strength.

Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies

Abstract: We review the theory and application of adiabatic exchange–correlation (xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations, respectively. Various different xc-kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self-energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.

Energetics of the coupled electronic–structural transition in the rare-earth nickelates

Abstract: Rare-earth nickelates exhibit a metal–insulator transition accompanied by a structural distortion that breaks the symmetry between formerly equivalent Ni sites. The quantitative theoretical description of this coupled electronic–structural instability is extremely challenging. Here, we address this issue by simultaneously taking into account both structural and electronic degrees of freedom using a charge self-consistent combination of density functional theory and dynamical mean-field theory, together with screened interaction parameters obtained from the constrained random phase approximation. Our total energy calculations show that the coupling to an electronic instability toward a charge disproportionated insulating state is crucial to stabilize the structural distortion, leading to a clear first order character of the coupled transition. The decreasing octahedral rotations across the series suppress this electronic instability and simultaneously increase the screening of the effective Coulomb interaction, thus weakening the correlation effects responsible for the metal–insulator transition. Our approach allows to obtain accurate values for the structural distortion and thus facilitates a comprehensive understanding, both qualitatively and quantitatively, of the complex interplay between structural properties and electronic correlation effects across the nickelate series.

Excited States of Molecules in Strong Uniform and Nonuniform Magnetic Fields.

Abstract: This paper reports an implementation of Hartree-Fock linear response with complex orbitals for computing electronic spectra of molecules in strong external magnetic fields. The implementation is completely general, allowing for spin-restricted, spin-unrestricted, and general two-component reference states. The method is applied to small molecules placed in strong uniform and nonuniform magnetic fields of astrochemical importance at the Random Phase Approximation level of theory. For uniform fields, where comparison is possible, the spectra are found to be qualitatively similar to those recently obtained with equation of motion coupled cluster theory. We also study the behavior of spin-forbidden excitations with progressive loss of spin symmetry induced by nonuniform magnetic fields. Finally, the equivalence of length and velocity gauges for oscillator strengths when using complex orbitals is investigated and found to hold numerically.

Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels

Abstract: We review the theory and application of adiabatic exchange-correlation (xc-) kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin's equations, respectively. Various different xc-kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self-energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.

Pairing in the Two-Dimensional Hubbard Model from Weak to Strong Coupling

Abstract: The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study the evolution of the leading superconducting instabilities of the single-orbital Hubbard model on a two-dimensional square lattice as a function of onsite Coulomb repulsion $U$ and band filling by calculating the irreducible particle-particle scattering vertex obtained from dynamical cluster approximation (DCA) calculations, and compare the results to both perturbative Kohn-Luttinger (KL) theory as well as the widely used random phase approximation (RPA) spin-fluctuation pairing scheme. Near half-filling we find remarkable agreement of the hierarchy of the leading pairing states between these three methods, implying adiabatic continuity between weak- and strong-coupling pairing solutions of the Hubbard model. The $d_{x^2-y^2}$-wave instability is robust to increasing $U$ near half-filling as expected. Away from half filling, the predictions of KL and RPA at small $U$ for transitions to other pair states agree with DCA at intermediate $U$ as well as recent diagrammatic Monte Carlo calculations. RPA results fail only in the very dilute limit, where it yields a $d_{xy}$ ground state instead of a $p$-wave state established by diagrammatic Monte Carlo and low-order perturbative methods, as well as our DCA calculations. We discuss the origins of this discrepancy, highlighting the crucial role of the vertex corrections neglected in the RPA approach. Overall, comparison of the various methods over the entire phase diagram strongly suggests a smooth crossover of the superconducting interaction generated by local Hubbard interactions between weak and strong coupling.

A Finite-Field Approach for GW Calculations beyond the Random Phase Approximation

Abstract: We describe a finite-field approach to compute density response functions, which allows for efficient G0 W0 and G0 W0Γ0 calculations beyond the random phase approximation. The method is easily applicable to density functional calculations performed with hybrid functionals. We present results for the electronic properties of molecules and solids, and we discuss a general scheme to overcome slow convergence of quasiparticle energies obtained from G0 W0Γ0 calculations, as a function of the basis set used to represent the dielectric matrix.

Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties

Abstract: We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in $^{208}\mathrm{Pb}$. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parametrization by ${\ensuremath{\chi}}^{2}$ minimization. This procedure is supplemented with the covariance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the ${\ensuremath{\chi}}^{2}$ minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies.

Nuclear electromagnetic dipole response with the self-consistent Green's function formalism

Abstract: Background: Microscopic calculations of the electromagnetic response of light and medium-mass nuclei are now feasible thanks to the availability of realistic nuclear interactions with accurate saturation and spectroscopic properties, and the development of large-scale computing methods for many-body physics. Purpose: To compute isovector dipole electromagnetic (E1) response and related quantities, i.e., integrated dipole cross section and polarizability, and compare with data from photoabsorption and Coulomb excitation experiments. To investigate the evolution pattern of the E1 response towards the neutron drip line with calculations of neutron-rich nuclei within a given isotopic chain. Methods: The single-particle propagator is obtained by solving the Dyson equation, where the self-energy includes correlations nonperturbatively through the algebraic diagrammatic construction (ADC) method. The particle-hole (ph) polarization propagator is treated in the dressed random phase approximation (DRPA), based on an effective correlated propagator that includes some 2p2h effects but keeps the same computation scaling as the standard Hartree-Fock propagator. Results: The E1 responses for 14,16,22,24O, 36,40,48,52,54,70Ca, and 68Ni have been computed: The presence of a soft dipole mode of excitation for neutron-rich nuclei is found, and there is a fair reproduction of the low-energy part of the experimental excitation spectrum. This is reflected in a good agreement with the empirical dipole polarizability values. The impact of different approximations to the correlated propagator used as input in the E1 response calculation is assessed. Conclusion: For a realistic interaction that accurately reproduces masses and radii, an effective propagator of the mean-field type computed by the self-consistent Green's function provides a good description of the empirical E1 response, especially in the low-energy part of the excitation spectrum and around the giant dipole resonance. The high-energy part of the spectrum improves and displays an enhancement of the strength when quasiparticle fragmentation is added to the reference propagator. However, this fragmentation (without a proper restoration of dynamical self-consistency) spoils the predictions of the energy centroid of the giant dipole resonance.

Vertex Corrections to the Polarizability Do Not Improve the GW Approximation for the Ionization Potential of Molecules.

Abstract: The GW approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree–Fock reference, ionization potentials predicted by the GW approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an in...

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

Abstract: Identification of the electronic state that appears upon doping a Mott insulator is important to understand the physics of cuprate high-temperature superconductors. Recent scanning tunneling microscopy of cuprates provides evidence that a charge-ordered state emerges before the superconducting state upon doping the parent compound. We study this phenomenon by computing the charge response function of the Hubbard model including frequency-dependent local vertex corrections that satisfy the compressibility sum rule. We find that upon approaching the Mott phase from the overdoped side, the charge fluctuations at wave vectors connecting hot spots are suppressed much faster than at the other wave vectors. It leads to a momentum dependence of the dressed charge susceptibility that is very different from either the bare susceptibility or from the susceptibility obtained from the random phase approximation. We also find that the paramagnetic lightly hole-doped Mott phase at finite temperature is unstable to charge ordering only at zero wave vector, confirming the results previously obtained from the compressibility. Charge order is driven by the frequency-dependent scattering processes that induce an attractive particle-hole interaction at large interaction strength and small doping.

Acoustic plasmons at the crossover between the collisionless and hydrodynamic regimes in two-dimensional electron liquids

Abstract: Hydrodynamic flow in two-dimensional electron systems has so far been probed only by dc transport and scanning gate microscopy measurements. In this work we discuss theoretically signatures of the hydrodynamic regime in near-field optical microscopy. We analyze the dispersion of acoustic plasmon modes in two-dimensional electron liquids using a non-local conductivity that takes into account the effects of (momentum-conserving) electron-electron collisions, (momentum-relaxing) electron-phonon and electron-impurity collisions, and many-body interactions beyond the celebrated Random Phase Approximation. We derive the dispersion and, most importantly, the damping of acoustic plasmon modes and their coupling to a near-field probe, identifying key experimental signatures of the crossover between collisionless and hydrodynamic regimes.

Relaxation Effects in Twisted Bilayer Graphene: a Multi-Scale Approach

Abstract: We introduce a multi-scale approach to obtain accurate atomic and electronic structures for atomically relaxed twisted bilayer graphene. High-level exact exchange and random phase approximation (EXX+RPA) correlation data provides the foundation to parametrize systematically improved force fields for molecular dynamic simulations that allow relaxing twisted layered graphene systems containing millions of atoms making possible a fine sweeping of twist angles. These relaxed atomic positions are used as input for tight-binding electronic band-structure calculations where the distance and angle-dependent interlayer hopping terms are extracted from density functional theory calculations and subsequent representation with Wannier orbitals. We benchmark our results against published force fields and widely used tight-binding models and discuss their impact in the spectrum around the flat band energies. We find that our relaxation scheme yields a magic angle of twisted bilayer graphene consistent with experiments between $1.0 \sim 1.1$ degree using commonly accepted Fermi velocities of graphene $v_F = 1.0 \sim 1.1 \times 10^6$ m/s that is enhanced by about 14%-20% compared with often used local density approximation estimates. Finally, we present high-resolution spectral function calculations for comparison with experimental ARPES. Additional force field parameters are provided for hBN-layered materials.

Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching

Abstract: Due to strong spin-orbit coupling, charge carriers in three-dimensionsal quadratic-band-touching Luttinger semimetals have nontrivial wave functions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric screening shows a reduced plasma frequency and an increased spectral weight at small wave vectors compared to a regular quadratic band. This weakens the effective Coulomb potential, modifying the single-particle self-energy for which we present both analytical and numerical results. At a low carrier density, the quasiparticle properties of this model strongly deviate from that of a single quadratic band. We compare our findings with experimental results for $\ensuremath{\alpha}$-Sn, HgSe, HgTe, YPtBi, and ${\mathrm{Pr}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$.

Measurements of the momentum-dependence of plasmonic excitations in matter around 1 Mbar using an X-ray free electron laser

Abstract: We present measurements of the plasmon shift in shock-compressed matter as a function of momentum transfer beyond the Fermi wavevector using an X-ray Free Electron Laser. We eliminate the elastically scattered signal retaining only the inelastic plasmon signal. Our plasmon dispersion agrees with both the random phase approximation (RPA) and static Local Field Corrections (sLFC) for an electron gas at both zero and finite temperature. Further, we find the inclusion of electron-ion collisions through the Born-Mermin Approximation (BMA) to have no effect. Whilst we cannot distinguish between RPA and sLFC within our error bars, our data suggest that dynamic effects should be included for LFC and provide a route forward for higher resolution future measurements.

RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods.

Abstract: We present a method to approximate post-Hartree-Fock correlation energies by using approximate natural orbitals obtained by the random phase approximation (RPA). We demonstrate the method by applying it to the helium atom, the hydrogen and fluorine molecule, and to diamond as an example of a periodic system. For these benchmark systems, we show that RPA natural orbitals converge the MP2 correlation energy rapidly. Additionally, we calculated full configuration interaction energies for He and H2, which are in excellent agreement with the literature and experimental values. We conclude that the proposed method may serve as a compromise to reach good approximations to correlation energies at moderate computational cost, and we expect the method to be especially useful for theoretical studies on surface chemistry by providing an efficient basis to correlated wave function based methods.

Optical response of Luttinger semimetals in the normal and superconducting states

Abstract: We investigate the optical response properties of three-dimensional Luttinger semimetals with the Fermi energy close to a quadratic band touching point. In particular, in order to address recent experiments on the spectroscopy of pyrochlore iridates and half-Heusler superconductors, we derive expressions for the optical conductivity in both the normal and general superconducting states in the linear response regime within the random phase approximation. The response functions can be decomposed into contributions from intraband and interband transitions, the latter comprising a genuine signature of the quadratic band touching point. We demonstrate the importance of interband transitions in the optical response in the normal state both in the homogeneous and quasistatic limit. Our analysis reveals a factorization property of the homogeneous conductivity in the spatially anisotropic case and the divergence of the conductivity for strong spatial anisotropy. In the quasistatic limit, the response is dominated by interband transitions and significantly different from systems with a single parabolic band. As an applications of the formalism in the superconducting state we compute the optical conductivity and superfluid density for the $s$-wave singlet superconducting case for both finite and vanishing chemical potential.

Competing superconducting phases in the interacting two-dimensional electron gas with strong Rashba spin-orbit coupling

Abstract: In this work, we study interacting electrons on a square lattice in the presence of strong Rashba spin-orbit interaction. The spin-orbit term forces the time-reversal electron states to be paired in even Cooper channels. For concreteness, we only consider the repulsive onsite Hubbard and nearest-neighbor Coulomb interactions, the so-called extended Hubbard model. To examine the superconducting instability, we obtain the effective interaction between electrons within the random phase approximation and treat the pairing instabilities driven by charge and spin fluctuations and their combined effects. We mapped out the phase diagram of the model in terms of interactions and electron fillings and found that while the ${d}_{xy}$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetries are the most likely pairing symmetries driven by charge and spin fluctuations, respectively, the strong effect of both fluctuations yields higher angular momentum Cooper instabilities. The possibility of topological superconductivity and triplet pairing is also discussed.

Screened Exchange Corrections to the Random Phase Approximation from Many-Body Perturbation Theory

Abstract: The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms that would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions, while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of second-order screened exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as [Formula: see text] or [Formula: see text] in orbital space or real space, respectively. Its memory requirement scales as [Formula: see text].

Low-Scaling Self-Consistent Minimization of a Density Matrix Based Random Phase Approximation Method in the Atomic Orbital Space.

Abstract: An efficient minimization of the random phase approximation (RPA) energy with respect to the one-particle density matrix in the atomic orbital space is presented. The problem of imposing full self-consistency on functionals depending on the potential itself is bypassed by approximating the RPA Hamiltonian on the basis of the well-known Hartree–Fock Hamiltonian making our self-consistent RPA method completely parameter-free. It is shown that the new method not only outperforms post-Kohn–Sham RPA in describing noncovalent interactions but also gives accurate dipole moments demonstrating the high quality of the calculated densities. Furthermore, the main drawback of atomic orbital based methods, in increasing the prefactor as compared to their canonical counterparts, is overcome by introducing Cholesky decomposed projectors allowing the use of large basis sets. Exploiting the locality of atomic and/or Cholesky orbitals enables us to present a self-consistent RPA method which shows asymptotically quadratic sc...

Dielectric function and plasmons of doped three-dimensional Luttinger semimetals

Abstract: Luttinger semimetals are three-dimensional electron systems with a parabolic band touching and an effective total spin $J=3/2$. In this paper, we present an analytical theory of dielectric screening of inversion-symmetric Luttinger semimetals with an arbitrary carrier density and conduction-valence effective mass asymmetry. Assuming a spherical approximation for the single-particle Luttinger Hamiltonian, we determine analytically the dielectric screening function in the random phase approximation for arbitrary values of the wave vector and frequency, the latter in the complex plane. We use this analytical expression to calculate the dispersion relation and Landau damping of the collective modes in the charge sector (i.e., plasmons).