Single-particle Green Function Research Articles

Light-driven electron transport through a molecular junction based on cross-conjugated systems.

This work explores light-driven electron transport through cross-conjugated molecules with different numbers of alkenyl groups. In the framework of coherent quantum transport, the analysis uses single-particle Green's functions together with non-Hermitian Floquet theory. With realistic parameters stemming from spectroscopy, the simulations show that measurable current (∼10(-11) A) caused by photon-assisted tunneling should be observed in a weak driving field (∼2 × 10(5) V/cm). Current-field intensity characteristics give one-photon and two-photon field amplitude power laws. The gap between the molecular orbital and the Fermi level of the electrodes is revealed by current-field frequency characteristics. Due to generalized parity symmetry, the cross-conjugated molecules with odd and even numbers of alkenyl groups exhibit completely different current-polarization characteristics, which may provide an advantageous feature in nanoelectronic applications.

Particle propagator of the spin Calogero–Sutherland model

Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero–Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the thermodynamic limit is also presented in detail. Combining this result with the hole propagator obtained in earlier studies, we calculate the spectral function of the single particle Green's function in the full range of the energy and momentum space. The resultant spectral function exhibits power-law singularity characteristic to correlated particle systems in one dimension.

Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations

We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to $2\ifmmode\times\else\texttimes\fi{}{18}^{2}$ sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the ${\mathbb{Z}}_{2}$ invariant and spin Chern number ${C}_{\ensuremath{\sigma}}$ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The ${\mathbb{Z}}_{2}$ invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the noninteracting limit, without any spontaneously symmetry breaking. The interaction-induced shift is nonperturbative in the interactions and cannot be captured within a ``simple'' self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the ${D}_{3}$ symmetry of the lattice, and destabilize topological phases when the one-body terms break the ${D}_{3}$ symmetry.

Quantum criticality in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction

We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like |\epsilon|^r at the Fermi energy (\epsilon=0) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to |\omega|^s. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<1/2 and 1/2<s<1, and applying the numerical renormalization-group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and \omega/T scaling in the dynamics that characterize an interacting critical point. The (r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum critical point.

Collective multipole excitations of exotic nuclei in relativistic continuum random phase approximation

The isoscalar and isovector collective multipole excitations in exotic nuclei are studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function. Different from the cases in stable nuclei, there are strong low-energy excitations in neutron-rich nuclei and proton-rich nuclei. The neutron or proton excess pushes the centroid of the strength function to lower energies and increases the fragmentation of the strength distribution. The effect of treating the contribution of continuum exactly is also discussed.

Density-matrix functionals from Green's functions

The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the one hand and theories based on many-body wave functions on the other. This link can be used to explicitly construct approximations for the density-matrix functional that are equivalent to standard diagrammatic re-summation techniques and to non-perturbative dynamical mean-field theory in particular. Contrary to functionals of the Green's-function, the exact density-matrix functional is convex and thus provides a true minimum principle which facilitates the calculation of the grand potential and derived equilibrium properties. The benefits of the proposed Green's-function-based density-matrix functional theory for geometrical structure optimization of strongly correlated materials are discussed.

Theory of electromagnetically induced transparency in strongly correlated quantum gases

We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with arbitrary inter-particle interaction strength. We show that, in the weak probe field limit, the EIT spectrum is solely determined by the single particle Green's function of the ground state atoms, and reflects interesting quantum many-body effects when atoms are virtually coupled to the low-lying Rydberg states. As an example, we apply our theory to 1D Luttinger liquid, Bose-Mott insulator state, and the superfluid state of two-component Fermi gases, and show how the many-body features can be observed non-destructively in the unconventional EIT spectrum.

Fluctuation-driven topological Hund insulators

We investigate the role of electron-electron interaction in a two-band Hubbard model based on the Bernevig-Hughes-Zhang Hamiltonian exhibiting the quantum spin Hall (QSH) effect. By means of dynamical mean-field theory, we find that a system with topologically trivial non-interacting parameters can be driven into a QSH phase at finite interaction strength by virtue of local dynamical fluctuations. For very strong interaction, the system reenters a trivial insulating phase by going through a Mott transition. We obtain the phase diagram of our model by direct calculation of the bulk topological invariant of the interacting system in terms of its single particle Green's function.

Green's function topology of Majorana wires

We represent the topological invariant characterizing a one-dimensional topological superconductor using a Wess–Zumino–Witten dimensional extension. The invariant is formulated in terms of the single-particle Green's function which allows us to classify interacting systems. Employing a recently proposed generalized Berry curvature method, the topological invariant is represented independent of the extra dimension requiring only the single-particle Green's function at zero frequency of the interacting system. Furthermore, a modified twisted boundary conditions approach is used to rigorously define the topological invariant for disordered interacting systems.

The Nuclear Incompressibility and Isoscalar Giant Dipole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant dipole resonance (ISGDR) in nuclei is studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. We employ different type interactions (NL1, NL3, NL3*, NL4, TM1, NLSH and PK1) corresponding to incompressibilities in the range 200–360 MeV. The results are discussed in comparison with the existing experimental data. It is found that the term can remove spurious components from the admixture of the center of mass state perfectly. The ISGDR distribution has two components, the lower-energy component and the higher-energy component. There is a large amount of very sharp peaks in the lower-energy region in RCRPA calculations. Only the higher-energy component is sensitive to the value of nuclear incompressibility employed in the calculations; the position of the lower-energy component is completely independent of the nuclear incompressibility Knm.

Real Space Green's Function Approach to Resonant Inelastic X-Ray Scattering and HERFD XAS

We present a theory of resonant inelastic x-ray scattering (RIXS) and high energy resolution fluorescence detected (HERFD) x-ray absorption spectra (XAS) based on the real space multiple scattering Green's function formalism. The Kramers-Heisenberg formula is transformed into an expression involving Single particle Green's functions. Simplifying assumptions give the RIXS cross section in terms of a convolution of an effective absorption spectrum with the x-ray emission spectrum. Given the RIXS cross section, calculations of the HERFD XAS are also possible. Self-energy effects are calculated using an efficient many-pole model. Further many-body effects can be treated via a convolution with an effective spectral function. The approach is implemented as an extension of the FEFF9 code. Calculated results are compared with experimental RIXS of WO2.

High Superconducting T c and Suppressed Isotope Effect in the Instantonic Condensate State of the Fermi-System: Analytic Solution

A superconducting pairing instability and iso- tope effect on the superconducting transition temperature Tc in the electronic system with instantonic condensate are derived analytically using previously proposed theory (Mukhin, J. Supercond. Nov. Magn. 22:75-80, 2009; J. Su- percond. Nov. Magn. 24:1165-1171, 2011) of the instan- tonic nature of the "hidden order" in high-Tc cuprates. The self-organized instantonic condensate breaks Matsub- ara "time" invariance of the Fermi-system, and occurs due to strongly nonlinear interaction between antiferromagnetic or charge density fluctuations. The Cooper-channel suscepti- bility (polarization loop) is calculated using a single-particle Green's function that we have derived recently (Mukhin and Galimzyanov, Physica B 407:1882-1884, 2012 )f or the Fermi-system with instantonic condensate. We found that superconducting Tc could be strongly enhanced and an iso- tope effect strongly suppressed in the presence of the instan- tonic condensate. The usual weak-coupling BCS results are recovered in the limit of vanishing the instantons. Relevance of the theoretical predictions for the high-Tc compounds is discussed.

Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study

We study a generalized Kane-Mele-Hubbard model with third-neighbor hopping, an interacting two-dimensional model with a topological phase transition as a function of third-neighbor hopping, by means of the determinant projector quantum Monte Carlo method. This technique is essentially numerically exact on models without a fermion sign problem, such as the one we consider. We determine the interaction dependence of the ${Z}_{2}$ topological insulator/trivial insulator phase boundary by calculating the ${Z}_{2}$ invariants directly from the single-particle Green's function. The interactions push the phase boundary to larger values of third-neighbor hopping, thus, stabilizing the topological phase. The observation of boundary shifting entirely stems from quantum fluctuations. We also identify qualitative features of the single-particle Green's function which are computationally useful in numerical searches for topological phase transitions without the need to compute the full topological invariant.

Nonequilibrium Green function approach to the pair distribution function of quantum many-body systems out of equilibrium

The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green functions—the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane—for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.

Absence of Luttinger’s Theorem due to Zeros in the Single-Particle Green Function

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, μ, for a T=0 gapped system is removed by using the unique value μ(T→0), Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the nonexistence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.

From the adiabatic theorem of quantum mechanics to topological states of matter

Abstractmagnified imageOwing to the enormous interest the rapidly growing field of topological states of matter (TSM) has attracted in recent years, the main focus of this review is on the theoretical foundations of TSM. Starting from the adiabatic theorem of quantum mechanics which we present from a geometrical perspective, the concept of TSM is introduced to distinguish gapped many body ground states that have representatives within the class of non‐interacting systems and mean field superconductors, respectively, regarding their global geometrical features. These classifying features are topological invariants defined in terms of the adiabatic curvature of these bulk insulating systems. We review the general classification of TSM in all symmetry classes in the framework of K‐Theory. Furthermore, we outline how interactions and disorder can be included into the theoretical framework of TSM by reformulating the relevant topological invariants in terms of the single particle Green's function and by introducing twisted boundary conditions, respectively. We finally integrate the field of TSM into a broader context by distinguishing TSM from the concept of topological order which has been introduced to study fractional quantum Hall systems. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Extended Skyrme interaction in the microscopic optical model of nucleon-nucleus scattering

The microscopic optical potential model based on calculations of the mass operator of the single-particle Green function has been refined by using the extended Skyrme-force variant, which involves additional both density- and momentum-dependent terms, and is employed for describing simultaneously properties of nuclei, nuclear-matter characteristics, and the nucleon-nucleus scattering observables in a self-consistent approach. From analyzing a differential cross section and polarization for a chosen case of the elastic neutron-nucleus scattering while controlling the characteristics of nuclear matter and finite-nuclei structure, a few sets of parameters have been determined for new variants of the extended Skyrme forces. It has been shown that the allowance for both the density- and momentum-dependent terms makes it possible to significantly improve the agreement with experimental data. The proposed extended Skyrme-force variants provide a satisfactory description for cross sections and analyzing powers of the neutron and proton scattering in a wide range of the target-nucleus mass numbers at different incident nucleon energies, as well as for a variety of nuclear structure characteristics.

Excitation spectra of the one-dimensional double-exchange model: An exact solution for one mobile electron

We study the one-dimensional double-exchange model with L localized spins and one mobile electron. We solve the Schrödinger equation analytically and obtain the energies and wave functions for all the eigenstates with spin S = (L − 1)***/2 exactly. As an application, we compute the single-particle Green's function. We show that, for vanishing exchange interactions between localized spins, the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass, i.e., the single electron is localized due to its interaction with the spin excitations. The analysis of the wave function gives us a particularly simple ground state.

A BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

Motivated by recent experimental and theoretical studies of excitonic insulators, we use the variational cluster approximation to calculate the single-particle Green's function and anomalous Green's function of the Falicov-Kimball model extended by including a finite valence bandwidth. We thus determine the single-particle excitation gap due to the bound-state formation of an electron and a hole. We also evaluate the order parameter of the excitonic insulating state indicating quantum coherence of condensed excitons. We thereby discuss the excitonic insulator that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime). A BCS-BEC crossover of the model thus manifests itself as a function of the Coulombic coupling strength.

Exact wave functions and excitation spectra of the one-dimensional double-exchange model with one mobile electron

Motivated by recent studies of the in-gap (or nonquasiparticle) states in the half-metallic ferromagnets, we study the one-dimensional double-exchange model with one mobile electron. We solve the Schrödinger equation analytically and obtain the energies and wave functions for all the eigenstates exactly. As an application, we compute the single-particle Green's function. We show that the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass; i.e., the single electron is localized due to its interaction with the spin excitations. Implication on the observed in-gap states in the half-metallic ferromagnets is considered.