Irreducible Interaction Research Articles

Improved effective vertices in the multiorbital two-particle self-consistent method from dynamical mean-field theory

In this paper, we present a multiorbital form of the two-particle self-consistent approach (TPSC) where the effective local and static irreducible interaction vertices are determined by means of the dynamical mean-field theory (DMFT). This approach replaces the approximate ansatz equations for the double-occupations $\ensuremath{\langle}{n}_{\ensuremath{\alpha},\ensuremath{\sigma}}^{}{n}_{\ensuremath{\beta},{\ensuremath{\sigma}}^{\ensuremath{'}}}^{}\ensuremath{\rangle}$ by sampling them directly for the same model using DMFT. Compared to the usual Hartree-Fock-like ansatz, this leads to more accurate local vertices in the weakly correlated regime and provides access to stronger correlated systems that were previously out of reach. This approach is extended by replacing the local component of the TPSC self-energy by the DMFT impurity self-energy, which results in an improved self-energy that incorporates strong local correlations but retains a nontrivial momentum dependence. We find that this combination of TPSC and DMFT provides a significant improvement over the multiorbital formulation of TPSC as it allows to determine the components of the spin vertex without artificial symmetry assumptions and opens the possibility to include the transversal particle-hole channel. The new approach is also able to remove unphysical divergences in the charge vertices in TPSC. We find a general trend that lower temperatures can be accessed in the calculation. Benchmarking single-particle quantities, such as the local spectral function with other many-body methods, we find significant improvement in the more strongly correlated regime.

A Pluralist Approach to Joint Responsibility

A Pluralist Approach to Joint Responsibility

Effect of Nonlocal Correlations on the Electronic Structure of LiFeAs.

We investigate the role of nonlocal correlations in LiFeAs by exploring an abinitio-derived multiorbital Hubbard model for LiFeAs via the two-particle self-consistent (TPSC) approach. The multiorbital formulation of TPSC approximates the irreducible interaction vertex to be an orbital-dependent constant, which is self-consistently determined from local spin and charge sum rules. Within this approach, we disentangle the contribution of local and nonlocal correlations in LiFeAs and show that in the local approximation one recovers the dynamical mean field theory result. The comparison of our theoretical results to most recent angular-resolved photoemission spectroscopy and de Haas-van Alphen data shows that nonlocal correlations in LiFeAs are decisive to describe the measured spectral function A(k[over →],ω), Fermi surface, and scattering rates. These findings underline the importance of nonlocal correlations and benchmark different theoretical approaches for iron-based superconductors.

Oracles and Query Lower Bounds in Generalised Probabilistic Theories

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), strong symmetry (existence of a rich set of nontrivial reversible transformations), and informationally consistent composition (roughly: the information capacity of a composite system is the sum of the capacities of its constituent subsystems). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, because fewer queries provide no information about the solution, then the corresponding “no-information” lower bound in theories lying at the kth level of Sorkin’s hierarchy is lceil {n/k}rceil . This lower bound leaves open the possibility that quantum oracles are less powerful than general probabilistic oracles, although it is not known whether the lower bound is achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource that might have power beyond that offered by quantum computation.

Deriving Grover's lower bound from simple physical principles

Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key resource behind this computational speed-up. However there is a limit to this interference, at most pairs of paths can ever interact in a fundamental way. Could more interference imply more computational power? Sorkin has defined a hierarchy of possible interference behaviours—currently under experimental investigation—where classical theory is at the first level of the hierarchy and quantum theory belongs to the second. Informally, the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. In this work, we consider how Grover's speed-up depends on the order of interference in a theory. Surprisingly, we show that the quadratic lower bound holds regardless of the order of interference. Thus, at least from the point of view of the search problem, post-quantum interference does not imply a computational speed-up over quantum theory.

Manifestation of the internal symmetry of irreducible triatomic interaction in the nonlinear properties of low-symmetry metals

A theory of the elastic moduli of crystals and amorphous substances is constructed that considers the internal symmetry of the irreducible energy of triatomic clusters. Allowing for the internal symmetry of clusters allows us to build three invariants by which the potential energy of any free triatomic cluster depends on the atomic coordinates. Direct calculation of the elastic modulus using an analytic form of the dependence of invariants on atomic coordinates shows that the adopted model leads to the following relationship between independent components of the third-rank elasticity tensor: $${C_{xx,\;yy,\;zz\;}} - ({C_{xx,\;yz,yz\;}} + {C_{yy,\;xz,\;xz\;}} + {C_{zz,\;xy,\;xy}}) + 2{C_{xy,\;yz,\;zx\;}} = 0$$ This result is independent of the global symmetry of a substance and represents a generalization of the widely known Caunhy discrepancies, which follow from models that consider only pair interactions. Fifteen laws of conservation that determine the movement of a point representing the atomic coordinates of cluster atoms in 9-dimensional configuration spaces of triatomic clusters are identified. The symmetry group of a triatomic cluster that determines these laws of conservation is identified.

Many-atom interactions in the theory of higher order elastic moduli: A general theory

The total potential energy of a crystal U({rik}) as a function of the vectors rik connecting centers of equilibrium positions of the ith and kth atoms is assumed to be represented as a sum of irreducible interaction energies in clusters containing pairs, triples, and quadruples of atoms located in sites of the crystal lattice A2: U({rik}) ≡ ΣN=14EN({rik}). The curly brackets denote the “entire set.” A complete set of invariants {Ij({rik})}N, which determine the energy of each individual cluster as a function of the vectors connecting centers of equilibrium positions of atoms in the cluster EN({rik}) ≡ EN({Ij({rik})}N), is obtained from symmetry considerations. The vectors rik are represented in the form of an expansion in the basis of the Bravais lattice. This makes it possible to represent the invariants {Ij({rik})}N in the form of polynomials of integers multiplied by τ2m. Here, τ2 is one-half of the edge of the unit cell in the A2 structure and m is a constant determined by the model of interaction energy in pairs, triples, and quadruples of atoms. The model interaction potential between atoms in the form of a sum of the Lennard-Jones interaction potential and similarly constructed interaction potentials of triples and quadruples of atoms is considered as an example. Within this model, analytical expressions for second-order and third-order elastic moduli of crystals with the A2 structure are obtained.

Monte Carlo study of the pairing interaction in the two-leg Hubbard ladder

Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility ξ( q) and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have d x 2− y 2- -like symmetry. The single-particle spectral weight is also shown to peak near (π,0) and (0,π) when the ratio of the inter- to intra-chain hopping t f t ≈ 1.5 , leading to an increased tendency for pairing.

Manyparticle interactions and local structure of the metallic hydrogen at zero pressure

On the basis of the perturbation expansion for electron gas energy in the third order to the electron-ion potential the pair and irreducible three-ion interaction potentials in metallic hydrogen are calculated. The irreducible potential of three-ion interaction has attractive nature at short interionic separation and oscillates at large ones. The anisotropic character of the three-ion interaction is shown. The potential relief of the pair ions relative to the third ion is constructed. This relief has some potential wells and valleys which connect them. The important role of the irreducible three-ion interaction in formation of the local order in three- and four-ion clusters is shown. The potential relief of an equiangular ion triplet relative to the fourth ion is calculated. This relief has deep potential well for fourth ion at interionic separation corresponding interproton separation in molecule $H_{2}$. The quasiclassical probability of ion transition into this well is evaluated. The life time of metallic phase of hydrogen relative to the tunneling nucleation of the $H_{2}$ molecules is estimated.

Dynamic susceptibility of the Hubbard-model calculated by expanding the irreducible interaction to second order in U

The magnetic dynamic susceptibility of the Hubbard-Model is calculated by expanding the irreducible interaction-part of the Bethe-Salpeter-Equation to second-order in U. The resulting collective modes differ in their dispersion from the RPA-result.

Spin-fluctuation mediated interaction in the two-dimensional Hubbard model

Using Monte Carlo results for the magnetic spin susceptibility and the irreducible electron-electron interaction, we argue that the exchange of para-antiferromagnetic spin fluctuations mediates the effective electron-electron interaction in the doped two-dimensional Hubbard model.

The effective electron-electron interaction in the 2D Hubbard model

Monte Carlo results for the irreducible particle-particle interaction in the two-dimensional Hubbard model are compared with a renormalized RPA single spin-fluctuation exchange interaction. Reasonable agreement is found for the parameter range which has been studied, giving support to the idea that the effective electron-electron interaction in the weak to moderately coupled Hubbard model arises from the exchange of single para-antiferromagnetic spin fluctuations.

Effective particle-particle interaction in the two-dimensional Hubbard model.

The irreducible particle-particle interaction Γ 1 of the two-dimensional Hubbard model is calculated by quantum Monte Carlo simulations. The Bethe-Salpeter equation for the pair-wave function is then solved using the Monte Carlo data for Γ 1 and the single-particle Green's function. The dominant pairing correlations in the intermediate-coupling regime and at small dopings are discussed

Comparison of Monte Carlo and diagrammatic calculations for the two-dimensional Hubbard model.

Monte Carlo results for a two-dimensional Hubbard model in the intermediate-coupling regime U=4t are compared with a diagrammatic spin-fluctuation approximation. Simulations on an 8\ifmmode\times\else\texttimes\fi{}8 lattice doped away from half filling were carried out down to temperatures of order 140 of the bandwidth. Results for the spin susceptibility \ensuremath{\chi}(q,i\ensuremath{\omega}${}_{\mathrm{m}}$), the electron self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}${}_{\mathrm{n}}$), various pair-field susceptibilities, and the irreducible particle-particle scattering vertex \ensuremath{\Gamma}(p\ensuremath{'},i\ensuremath{\omega}${}_{\mathrm{n}\ensuremath{'}}$|p,i\ensuremath{\omega}${}_{\mathrm{n}}$) were obtained. A random-phase approximation for \ensuremath{\chi}(q,i\ensuremath{\omega}${}_{\mathrm{m}}$) with a renormalized Coulomb coupling U\ifmmode\bar\else\textasciimacron\fi{} is shown to provide a fit to the Monte Carlo data. A similar approximation for the Berk-Schrieffer spin-fluctuation interaction also provides a reasonable fit to the self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}${}_{\mathrm{n}}$) in the region explored by the Monte Carlo data. However, a similar approximation for the irreducible particle-particle interaction failed to reproduce the Monte Carlo results. Higher-order vertex corrections were calculated, but significant discrepancies with Monte Carlo results for \ensuremath{\Gamma} remain.

Plasmon Mechanism of Superconductivity in the Multivalley Electron Gas

The Eliashberg equation is solved in both frequency and momentum variables to obtain the superconducting transition temperature T c in the multivalley electron gas without phonons. Both the one-particle Green's function and irreducible two-electron interaction are evaluated in the random-phase approximation which provides exact results in the limit of large valley degeneracy g v and is known to give sufficiently accurate ones even for g v as small as 3 or 4. Among s -, p -, and d -waves, the s -wave pairing is most stable for g v ≥2 with a fairly high T c . For g v ≫1, our solution is reduced to “bipolaronic superconductivity”. We discuss implications of the present results to the exotic superconductors with relatively low carrier concentration.

Correlations in fully-spin-polarized liquid 3He: Ladders, rings, and the particle-hole irreducible interaction.

We investigate the relative contribution of ladder and ring diagrams to the single-particle self-energy in fully-spin-polarized liquid $^{3}\mathrm{He}$ ${(}^{3}$${\mathrm{He}}^{\mathrm{\ensuremath{\uparrow}}}$). Ladder diagrams are summed to all orders of the bare $^{3}\mathrm{\ensuremath{-}}^{3}$He interaction using the Galitskii-Feynman-Hartree-Fock (GFHF) analysis. Previous studies of $^{3}\mathrm{He}^{\mathrm{\ensuremath{\uparrow}}}$, using GFHF analysis, have neglected the part of the GFHF self-energy coming from the correlation potential, ${\mathit{V}}_{\mathrm{co}}$. These calculations produced ground-state energies in fair agreement with values obtained from variational Monte Carlo (VMC) calculations. However, properties such as Landau parameters, which are directly related to long-range correlations, tend to differ considerably from known values. In the present work we have evaluated ${\mathit{V}}_{\mathrm{co}}$ and found it to have an appreciable effect on the single-particle excitation energies, \ensuremath{\varepsilon}(k) and the ground-state energy: Including ${\mathit{V}}_{\mathrm{co}}$ significantly reduces the ground-state energy. As a further refinement over previous GFHF calculations, we have used a more accurate center-of-mass momentum, P, dependence for the Galitskii-Feynman t matrix in the self-energy calculation. Again we find an undesirably large decrease in the ground-state energy. Finally, upon including a contribution from a summation of ring diagrams, we find a ground-state energy that is once again in fair agreement with the VMC values. The ring diagrams are driven by a local particle-hole interaction obtained by the method of correlated basis functions (CBF). Ring diagrams are then summed within a random-phase approximation. Our final \ensuremath{\varepsilon}(k) is used to calculate the particle-hole irreducible interaction ${\mathit{I}}_{\mathit{p}\mathrm{\ensuremath{-}}\mathit{h}}$. In the long-wavelength limit we find that our ${\mathit{I}}_{\mathit{p}\mathrm{\ensuremath{-}}\mathit{h}}$ is in much better agreement with the CBF ${\mathit{I}}_{\mathit{p}\mathrm{\ensuremath{-}}\mathit{h}}$ when our \ensuremath{\varepsilon}(k) includes contributions from ${\mathit{V}}_{\mathrm{co}}$, ${\mathrm{\ensuremath{\Sigma}}}_{\mathit{R}}$, and the refined self-energy calculation.

Dynamics and particle-hole interactions in liquid 3He: A Green's-function approach.

The dynamics of normal and fully spin-polarized $^{3}\mathrm{He}$ are studied for momentum transfers below 2 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$. This study is based on a first-principles calculation of the dynamic susceptibility, \ensuremath{\chi}(Q,\ensuremath{\omega}). We invoke the Baym and Kadanoff (BK) procedure for generating an approximate particle-hole irreducible interaction, ${\mathit{I}}_{\mathrm{ph}}$, which is needed in the calculation of \ensuremath{\chi}(Q,\ensuremath{\omega}). The BK procedure yields an ${\mathit{I}}_{\mathrm{ph}}$ that conserves particle number, energy, and momentum. When the BK procedure is applied to the Galitskii-Feynman-Hartree-Fock (GFHF) self-energy, the resulting ${\mathit{I}}_{\mathrm{ph}}$ consists of direct and induced terms. Previous calculations using GFHF theory have neglected induced effects. For Q2 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$, the induced term contributes significantly to the strength of ${\mathit{I}}_{\mathrm{ph}}$. Landau parameters calculated with induced effects included are greatly improved. We compare our (static) ${\mathit{I}}_{\mathrm{ph}}$ to those obtained from other first-principles calculations, from polarization-potential theories, and from the available experimental data. In spin-polarized $^{3}\mathrm{He}$, we find that ${\mathit{I}}_{\mathrm{ph}}$ is strongly density dependent. In normal $^{3}\mathrm{He}$, the same behavior is observed for the spin-symmetric contribution. In contrast, the spin-antisymmetric contribution is nearly independent of density. This finding is in agreement with experiment. For both systems a well-defined zero-sound mode was determined. Using our microscopically determined ${\mathit{I}}_{\mathrm{ph}}$, effective mass, Landau parameter ${\mathit{F}}_{1}^{\mathit{s}}$, and a polarization-potential form for the frequency dependence of ${\mathit{I}}_{\mathrm{ph}}$, we obtained a zero-sound dispersion that agrees well at low Q with the experimentally determined one. Finally, we comment on the relevance of the spin-fluctuation contribution observed in our ${\mathit{I}}_{\mathrm{ph}}$ for the case of normal $^{3}\mathrm{He}$.

A new interpolation between long- and short range correlations in an electron liquid. I. Diagrammatic consideration of the local field corrections

On the basis of the diagrammatic method, a new interpolation between long- and short-range correlations in an electron liquid is presented. In the interpolation scheme, the spin-parallel and spin-antiparallel correlations are studied separately. The authors evaluate numerically the local-field factor from short-range Coulomb repulsion by solving the integral equation for the particle-particle ladder interaction. The irreducible particle-hole interaction is constructed from an approximation interpolation between the RPA dynamically screened Coulomb interaction and the ladder interaction. The local-field factor from the exchange interaction is evaluated from the exchange polarisation function of lowest order in this irreducible particle-hole interaction. An interrelation between the two local-field factors is discussed.

The irreducible three-body interaction between three ions in a solvent

The irreducible potential of average force between three ions in a dipolar solvent is found for an equilateral triangular configuration. The interaction falls off asymptotically as R −4 at large distances.

Three-quark interaction: The driving force in the inhomogeneous evolution equations

Using perturbative QCD on the light cone (A/sub +/ = 0 gauge), and the Brodsky-Lepage collinear projection, we make a partial-wave projection (in the l/sub z/ component) of the Weinberg equation, and find a set of evolution equations for distribution amplitudes. For l/sub z/not =0 our equations are inhomogeneous, and their solutions show an increasing QCD perturbative effect for the currently available momentum transfers. The driving force of the inhomogenous evolution equations is a three-quark irreducible interaction, which gives terms approx.(1-x)/sup 3/ in the proton's deep-inelastic structure function, breaks the SU(6) symmetry, and contributes to the deviation of the d/u ratio for proton from the value 1/2. That force couples a qq-bar pair to one transverse gluon and one Coulomb gluon.