Summation Of Ladder Diagrams Research Articles

Multiband dual fermion approach to quantum criticality in the Hubbard honeycomb lattice

We study the Hubbard model on the honeycomb lattice in the vicinity of the quantum critical point by means of a multiband formulation of the Dual Fermion approach. Beyond the strong local correlations of the dynamical mean field, critical fluctuations on all length scales are included by means of a ladder diagram summation. Analysis of the susceptibility yields an estimate of the critical interaction strength of the quantum phase transition from a paramagnetic semimetal to an antiferromagnetic insulator, in good agreement to other numerical methods. We further estimate the crossover temperature to the renormalized classical regime. Our data imply that, at large interaction strengths, the Hubbard model on the honeycomb lattice behaves like a quantum nonlinear sigma model, while being in a non-Fermi liquid state.

Effect of vertex corrections on the possibility of chiral symmetry breaking induced by long-range Coulomb repulsion in graphene

In this paper, we consider the possibility of chiral (charge or spin density wave) symmetry breaking in graphene due to long-range Coulomb interaction by comparing the results of the Bethe-Salpeter and functional renormalization-group approaches. The former approach performs a summation of ladder diagrams in the particle-hole channel and reproduces the results of the Schwinger-Dyson approach for the critical interaction strength of the quantum phase transition. The renormalization-group approach combines the effect of different channels and allows to study the role of vertex corrections. The critical interaction strength, which is necessary to induce the symmetry breaking in the latter approach, is found in the static approximation to be ${\ensuremath{\alpha}}_{c}={e}^{2}/(\ensuremath{\epsilon}{v}_{F})\ensuremath{\approx}1.05$ without considering the Fermi velocity renormalization, and ${\ensuremath{\alpha}}_{c}=3.7$ with accounting the renormailzation of the Fermi velocity. The latter value is expected to be, however, reduced, when the dynamic screening effects are taken into account, yielding the critical interaction, which may be comparable to the one in freely suspended graphene. We show that the vertex corrections are crucially important to obtain the mentioned values of critical interactions.

Strong-coupling phases of 3D Dirac and Weyl semimetals. A renormalization group approach

We investigate the strong-coupling phases that may arise in 3D Dirac and Weyl semimetals under the effect of the long-range Coulomb interaction, considering the many-body theory of these electron systems as a variant of the conventional fully relativistic Quantum Electrodynamics (QED). For this purpose, we apply two different nonperturba-tive approaches, consisting in the sum of ladder diagrams and taking the limit of a large number N of fermion flavors. We benefit from the renormalizability that the theory shows in both cases to compute the anomalous scaling dimensions of different operators exclusively in terms of the renormalized coupling constant, allowing us to determine the precise location of the singularities signaling the onset of the strong-coupling phases. We show then that the QED of 3D Dirac semimetals has two competing effects at strong coupling. One of them is the tendency to chiral symmetry breaking and dynamical mass generation, which are analogous to the same phenomena arising in the conventional QED at strong coupling. This trend is however outweighed by the strong suppression of electron quasiparticles that takes place at large N , leading to a different type of critical point at sufficiently large interaction strength, shared also by the 3D Weyl semimetals. Overall, the phase diagram of the 3D Dirac semimetals turns out to be richer than that of their 2D counterparts, displaying a transition to a phase with non-Fermi liquid behavior which may be observed in materials hosting a sufficiently large number of Dirac or Weyl points.

Finite-temperature line shapes of hard-core bosons in quantum magnets: A diagrammatic approach tested in one dimension

The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here, we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line shape is found to be asymmetric at elevated temperatures and the bandwidth of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced that can also be applied to more sophisticated and higher dimensional models.

Ground-state phases of ultracold bosons with Rashba-Dresselhaus spin-orbit coupling

We study ultracold bosons in three dimensions with an anisotropic Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation of ladder diagrams for the two-boson t-matrix at zero energy. Then, with the t-matrix as the effective interaction, we find the ground-state phase diagrams of bosons in mean field as a function of the spin-orbit coupling, the anisotropy, and the scattering lengths between particles in the same and in different pseudospin states. The resulting phase diagrams have much richer structures than those obtained using mean-field couplings, exhibiting three different phases: a plane-wave condensate, a striped condensate, and an unstable phase. The differences between the present approach using the t-matrix compared to using mean-field couplings is significant for large scattering lengths, large spin-orbit-coupling strength, or small anisotropy.

Low-energy excitations and singular contributions in the thermodynamics of clean Fermi liquids

Using a recently suggested method of bosonization in an arbitrary dimension, we study the anomalous contribution of the low energy spin and charge excitations to thermodynamic quantities of a two-dimensional (2D) Fermi liquid. The method is slightly modified for the present purpose such that the effective supersymmetric action no longer contains the high energy degrees of freedom but still accounts for effects of the finite curvature of the Fermi surface. Calculating the anomalous contribution $\delta c(T)$ to the specific heat, we show that the leading logarithmic in temperature corrections to $\delta c(T)/T^2$ can be obtained in a scheme combining a summation of ladder diagrams and renormalization group equations. The final result is represented as the sum of two separate terms that can be interpreted as coming from singlet and triplet superconducting excitations. The latter may diverge in certain regions of the coupling constants, which should correspond to the formation of triplet Cooper pairs.

Confinement property in SU(3) gauge theory

We study the confinement property of the pure SU(3) gauge theory, combining in this effort the nonperturbative gluon and ghost propagators obtained as solutions of Dyson-Schwinger equations with solutions of an integral ladder diagram summation type equation for the Wilson loop. We obtain the string potential and effective UV coupling.

Pairing properties of nucleonic matter employing dressed nucleons

A survey of pairing properties of nucleonic matter is presented that includes the off-shell propagation associated with short-range and tensor correlations. For this purpose, the gap equation has been solved in its most general form employing the complete energy and momentum dependence of the normal self-energy contributions. The latter correlations include the self-consistent calculation of the nucleon self-energy that is generated by the summation of ladder diagrams. This treatment preserves the conservation of particle number unlike approaches in which the self-energy is based on the Brueckner-Hartree-Fock approximation. A huge reduction in the strength as well as temperature and density range of ${}^3S_1$-${}^3D_1$ pairing is obtained for nuclear matter as compared to the standard BCS treatment. Similar dramatic results pertain to ${}^1S_0$ pairing of neutrons in neutron matter.

Effect of electron-phonon interaction on the resistivity of metallic nanowires

Using a tight-binding approach for the electronic structure, deformation potential approach for the electron-phonon interaction, and the Kubo formula for the conductivity, an expression has been obtained for the resistivity of nanowire systems. The resulting expression involves (1) vertex corrections approximated by the sum of ladder diagrams, and (2) a self-energy approximated by the one-phonon processes. The dependence of the resistivity on the wire width, temperature and Fermi energy has been investigated by performing numerical calculations in terms of typical values of different parameters. It has been found that the resistivity increases with decreasing wire width. It has been further found that the resistivity increases with the temperature such that the resistivity slope increases with decreasing wire width. The temperature dependence shows a superlinear behavior for wires of width \ensuremath{\sim}20 nm. For wires of larger widths a linear behavior has been found. The resistivity is found to increase slowly with the Fermi energy. The relevance of the calculated results has been discussed in light of the existing experimental studies.

Correlation dynamics of Green functions

We generalize the methods used in the theory of correlation dynamics and establish a set of equations of motion for many-body correlation Green functions in the nonrelativistic case. These nonlinear and coupled equations of motion describe the dynamical evolution of correlation Green functions of different order and transparently show how many-body correlations are generated by the different interaction terms in a genuine nonperturbative framework. The nonperturbative results of the conventional Green function theory are included in the present formalism as two limiting cases (the so-called ladder-diagram summation and ring-diagram summation) as well as the familiar correlation dynamics of density matrices in the equal-time limit. We present explicit expressions for three- and four-body correlation functions that can be used to dynamically restore the trace relations for spin-symmetric Fermi systems and study numerically the relative importance of two-, three- and four-body correlations for nuclear configurations close to the ground state.

High energy, large momentum transfer amplitudes: The sum of ladder diagrams inΦ 3 theory

We perform summation of ladder diagrams in the high energy, large momentum limit. This leads to new results for both perturbative and non-perturbative approaches. In particular, an explicit expression for any diagram's contribution is given, the non-perturbative form of asymptotically non-analytic terms is found and representation of amplitude as a series of Regge poles is presented.

Transverse spin and higher twist in QCD

A complete, but non-standard, parton model description is made for transverse-spin effects in hadronic interactions. The Q 2 dependence of the various structure functions involved (corresponding to operators of both twist two and three) is evaluated to leading-logarithmic order via the ladder-diagram summation technique.

Two-nucleon correlations in a relativistic theory of nuclear matter

Relativistic two-nucleon correlations are studied using a self-consistent summation of ladder diagrams in nuclear matter. Correlations have a small effect on the nucleon self-energy but may produce significant changes in the binding energy. Correlation corrections to the mean-field equation of state are small at high density.

Weak absence of diffusion in two dimensions in the weak-disorder limit

Working within the single-electron picture of two-dimensional disordered systems in the crucial weak-disorder regime, the authors calculate the average two-particle Green function by summing the maximally crossed diagrams occurring in the approximation of Neal and Langer (1966) as developed by Abrahams and Ramakrishnan (1980) to show that Anderson's criterion for location is not satisfied, while there is only a weak absence of diffusion in the sense of Ishii (1973). Summation of ladder diagrams appearing in the Langer-Neal scheme gives an identical result in the small-disorder regime. They reach the same conclusion upon using the CPA to perform the required averaging. Recent mathematical results associate such a weak absence of diffusion with a singularly continuous spectrum.

A consistent treatment of spin dependence at high energies in an eikonal picture of pp elastic scattering

We present an improved theoretical eikonal model for the spin dependence in scattering at very high energies. The model corresponds to a unitarity-type sum of ladder diagrams, and the resultant spin structure has quite remarkable properties.

Electron Correlations and Dielectric Function of Electron Gas at Metallic Densities

Short-range correlations in an electron gas are investigated from a diagrammatic analysis of perturbation theory. An infinite sum of electron-electron ladder diagrams is shown to be indispensable for the short-range correlation at metallic densities. A new approximate expression for the dielectric function e ( q ,ω) is presented, which is an interpolation between the random phase approximation (RPA) for small q and an infinite sum of ladder diagrams between electrons with antiparallel spins for large q .

High-energy summation of ladder diagrams in nonpolynomial field theories

The leading high-energy behavior of the sum of ladder diagrams is discussed in local and nonlocal field theories of nonpolynomial type. It is shown that the complete amplitude satisfies an integral equation of Volterra type at high-energy and in several cases it possesses Regge-behaved upper bounds. This high-energy behavior is confirmed also model calculations.

Equivalence of Perturbation-Theory Techniques and the Bethe-Salpeter Equation for Summing Feynman Diagrams

Polkinghorne's exact perturbation-theory equation for the leading Regge trajectory resulting from an infinite sum of ladder diagrams is shown to be mathematically equivalent to the partial-wave Bethe-Salpeter equation. Thus, the perturbation-theory equation can be used not only for the leading Regge trajectory, but for all secondary trajectories as well.

The diagram technique in the theory of multiple scattering

A quantum-mechanical approach is used to obtain an analytic solution of the multiple-scattering problem for neutrons. A graphic representation is obtained for the average transition probability. This average transition probability is represented by the sum of ladder diagrams each of which describes a certain number of scattering processes. For the case of an infinite slab the ratio ofn-times scattered neutron intensity to (n−1)-times scattered neutron intensity has been calculated.

A simple model containing daughters

A simple model, related to the sum of ladder diagrams, is shown to contain a parent Regge trajectory with its daughter, grand-daughter etc., and no others. Other trajectories can be introduced by making modifications to the model.