Particle Green Function Research Articles

Probing single electron scattering through a non-Fermi-liquid charge-Kondo device

Among the exotic and yet unobserved features of multichannel Kondo impurity models is their subunitary single electron scattering. In the two-channel Kondo model, for example, an incoming electron is fully scattered into a many-body excitation such that the single particle Green's function vanishes. Here, we propose to directly observe these features in a charge-Kondo device encapsulated in a Mach-Zehnder interferometer, within a device already studied by Duprez et al. [Science 366, 1243 (2019)]. We provide detailed predictions for the visibility and phase of the Aharonov-Bohm oscillations depending on the number of coupled channels and the asymmetry of their couplings.

Low energy excitation spectrum of magic-angle semimetals

We theoretically study the excitation spectrum of a two-dimensional Dirac semimetal in the presence of an incommensurate potential. Such models have been shown to possess magic-angle critical points in the single particle wavefunctions, signalled by a momentum space delocalization of plane wave eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the kernel polynomial method, we compute the single particle Green's function to extract the nature of the single particle excitation energy, damping rate, and quasiparticle residue. As a result, we are able to clearly demonstrate the redistribution of spectral weight due to quasiperiodicity-induced downfolding of the Brillouin zone creating minibands with effective mini Brillouin zones that correspond to emergent superlattices. By computing the damping rate we show that the vanishing of the velocity and generation of finite density of states at the magic-angle transition coincides with the development of an imaginary part in the self energy and a suppression of the quasiparticle residue that vanishes in a power law like fashion. Observing these effects with ultracold atoms using momentum resolved radiofrequency spectroscopy is discussed.

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe-Salpeter equation calculations of molecules.

The ab initio GW plus Bethe-Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn-Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm-Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn-Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel's set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson–Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1≤c≤0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration cp. The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

Exact description of quantum stochastic models as quantum resistors

We study the transport properties of generic out-of-equilibrium quantum systems connected to fermionic reservoirs. We develop a new method, based on an expansion of the current in terms of the inverse system size and out of equilibrium formulations such as the Keldysh technique and the Meir-Wingreen formula. Our method allows a simple and compact derivation of the current for a large class of systems showing diffusive/ohmic behavior. In addition, we obtain exact solutions for a large class of quantum stochastic Hamiltonians (QSHs) with time and space dependent noise, using a self consistent Born diagrammatic method in the Keldysh representation. We show that these QSHs exhibit diffusive regimes which are encoded in the Keldysh component of the single particle Green's function. The exact solution for these QSHs models confirms the validity of our system size expansion ansatz, and its efficiency in capturing the transport properties. We consider in particular three fermionic models: i) a model with local dephasing ii) the quantum simple symmetric exclusion process model iii) a model with long-range stochastic hopping. For i) and ii) we compute the full temperature and dephasing dependence of the conductance of the system, both for two- and four-points measurements. Our solution gives access to the regime of finite temperature of the reservoirs which could not be obtained by previous approaches. For iii), we unveil a novel ballistic-to-diffusive transition governed by the range and the nature (quantum or classical) of the hopping. As a by-product, our approach equally describes the mean behavior of quantum systems under continuous measurement.

Local density of states and scattering rates across the many-body localization transition

Characterizing the many-body localization (MBL) transition in strongly disordered and interacting quantum systems is an important issue in the field of condensed matter physics. We study the single particle Green's functions for a disordered interacting system in one dimension using exact diagnonalization in the infinite temperature limit and provide strong evidence that single particle excitations carry signatures of delocalization to MBL transition. In the delocalized phase, the typical values of the local density of states and the scattering rate are finite while in the MBL phase, the typical values for both the quantities become vanishingly small. The probability distribution functions of the local density of states and the scattering rate are broad log-normal distributions in the delocalized phase while the distributions become very narrow and sharply peaked close to zero in the MBL phase. We also study the eigenstate Green's function for all the many-body eigenstates and demonstrate that both, the energy resolved typical scattering rate and the typical local density of states, can track the many-body mobility edges.

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

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

BetheSF V2: 3-point propagator and additional external potentials

In a recent paper (Comput. Phys. Commun. 258 (2021) 107569) we obtained exactly the tagged-particle propagator in a single-file with N particels diffusing in a generic confining potential via the coordinate Bethe-Ansatz. A naïve implementation of this solution requires a non-polynomial algorithm. To speed-up the computation we implemented a more efficient algorithm that exploits the particle exchange-symmetry.In this new version we expand the code-base to allow for the computation of the three point Green's function. The latter is required e.g. in the analysis of the breaking of time-translational invariance. In addition we include the support for two canonical potentials of general interest: one presenting an energy barrier and one featuring an asymmetric potential landscape. New version program summaryProgram Title: BetheSFCPC Library link to program files:https://doi.org/10.17632/3bs74vf72n.2Licensing provisions: MITProgramming language: C++ (C++17 required), Boost 1.75.0 requiredJournal reference of previous version: Comput. Phys. Commun. 258 (2021) 107569Does the new version supersede the previous version?: YesReasons for new version: Computation of the three point Green's function, vectorized versions of the Green's functions, two new potentials included.Nature of problem: Diffusive single-files are mathematical models of effectively one-dimensional strongly correlated many-body systems. The diffusive dynamics of a tracer particle in a single-file has attracted widespread interest in the literature since it stands as a paradigm for non-Markovian and anomalous diffusion. The many-body Fokker-Planck equation governing the system's dynamics can be solved using the Coordinate Bethe Ansatz. The implementation of such a solution is notoriously challenging since it requires the generation of permutations.Solution method: Exploiting the underlining exchange symmetry among the particles of the system, it is possible to reduce the complexity of the algorithm for evaluating the tagged particle Green's function, in the best gain scenario, from O(N!) down to O(N), N being the size of the single-file.Summary of revisions:•We added support for the computation of the three point Green's function:G(xi,ta+τ;xi′,ta|x0i)=V00(x0i)−1∑k∑lV0k(xi)Vkl(xi′)Vl0(x0i)e−Λkτe−Λlta. Where the overlap elements Vkl(x) and the many-body eigenvalues Λk have been defined in the main article [1]. This function expresses the probability of the tagged-particle to end up in xi at time ta+τ, passing by xi′ and time ta conditioned to the fact that it started in x0i at time 0. This function is important for the study of breaking of the time-translation invariance in tagged particle dynamics [2]. Due to the presence of the term Vkl(x) the evaluation is time expensive. The code has been modified to allow for the computation of G(xi,ta+τ;xi′,ta|x0i).•We added functions that compute the two and the three point Green's functions at M different time-points but with the same spatial parameters. These new vectorized versions return a std::vector<double> containing the values of the Green's functions for several time-points. A single call of one of these new fuctions is faster than calling M times the corresponding previously implemented single-time-point function.•Solution for the square double well potential [3](1)U(x)={0,π>|x|>π/2f0,|x|≤π/2∞,otherwise; and for the asymmetric potential given by [4]:(2)U(x)=−(h−1)ln⁡(x)+x22 have been added in the files SingleFileBistable.hpp, SingleFileBistable.cpp and SingleFileGeneralizedBessel.hpp, SingleFileGeneralizedBessel.cpp respectively; the potentials are depicted in Fig. 1. The solution for the potential in Eq. (2) requires the computation of “special functions” related to the Gamma function and the hypergeometric function; these functions are provided either by the Boost library or can be found as template functions in the SpecialFunctions.hpp file. The potential (1) has been investigated in [3].

Impurities in systems of noninteracting trapped fermions

We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-Péché (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.

Bosonization of the Q=0 continuum of Dirac fermions

We develop a bosonization formalism that captures non-perturbatively the interaction effects on the $\mathbf{Q}=0$ continuum of excitations of nodal fermions above one dimension. Our approach is a natural extension of the classic bosonization scheme for higher dimensional Fermi surfaces to include the $\mathbf{Q}=0$ neutral excitations that would be absent in a single-band system. The problem is reduced to solving a boson bilinear Hamiltonian. We establish a rigorous microscopic footing for this approach by showing that the solution of such boson bilinear Hamiltonian is exactly equivalent to performing the infinite sum of Feynman diagrams associated with the Kadanoff-Baym particle-hole propagator that arises from the self-consistent Hartree-Fock approximation to the single particle Green's function. We apply this machinery to compute the interaction corrections to the optical conductivity of 2D Dirac Fermions with Coulomb interactions reproducing the results of perturbative renormalization group at weak coupling and extending them to the strong coupling regime.

Transient Anomalous Diffusion in a Heterogeneous Environment

This work provides an analytical model for the diffusive motion of particles in a heterogeneous environment where the diffusivity varies with position. The model for diffusivity describes the environment as being homogeneous with randomly positioned pockets of larger diffusivity. This general framework for heterogeneity is amenable to a systematic expansion of the Green's function, and we employ a diagrammatic approach to identify common terms in this expansion. Upon collecting a common family of these diagrams, we arrive at an analytical expression for the particle Green's function that captures the spatially varying diffusivity. The resulting Green's function is used to analyze anomalous diffusion and kurtosis for varying levels of heterogeneity, and we compare these results with numerical simulations to confirm their validity. These results act as a basis for analysis of a range of diffusive phenomena in heterogeneous materials and living cells.

Nonequilibrium Green's functions and their relation to the negative differential conductance in the interacting resonant level model

We evaluate the non-equilibrium single particle Green's functions in the steady state of the interacting resonant level model (IRLM) under the effect of an applied bias voltage. Employing the so-called auxiliary master equation approach, we present accurate nonperturbative results for the non-equilibrium spectral and effective distribution functions, as well as for the current-voltage characteristics. We find a drastic change of these spectral properties between the regimes of low and high bias voltages and discuss the relation of these changes to the negative differential conductance (NDC), a prominent feature in the non-equilibrium IRLM. The anomalous evolution of the distribution function next to the impurity shown by our calculations suggests a mechanism whereby the impurity gets effectively decoupled from the leads at voltages where the NDC sets in, in agreement with previous renormalization group approaches. This scenario is qualitatively confirmed by a Hartree-Fock treatment of the model.

Exact and quasiclassical Green's functions of two-dimensional electron gas with Rashba–Dresselhaus spin–orbit interaction in parallel magnetic field

New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba–Dresselhaus spin–orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that allows an exact analytical solution is also highlighted. To demonstrate the advantages of our approach we apply the obtained Green's function to calculation of electron density and magnetization.

Variational treatment of electron–polyatomic-molecule scattering calculations using adaptive overset grids

The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory is shown to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has rapid convergence properties, both in the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF$_4$ in the static-exchange approximation, and compared in detail with calculations performed with the numerical Schwinger variational approach based on single center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Auxiliary fermion approach to the resonant inelastic x-ray scattering response in an underdoped cuprate

We describe a method for calculating the resonant inelastic X-ray scattering (RIXS) response---including the dynamics of the transient core hole---of many-body systems with non-trivial gap structure encoded in their single particle Green's function. Our approach introduces auxiliary fermions in order to obtain a form amenable to the determinant method of Benjamin et al. [PRL 112 247002 (2014)], and is applicable to systems where interactions are most strongly felt through a renormalization of the single particle propagator. As a test case we consider the Yang Rice Zhang ansatz describing cuprate phenomena in the underdoped `pseudogap' regime, and show that including the core hole dynamics pushes the RIXS peaks towards higher energy transfer, improving agreement with experiments.

Single-particle excitations in disordered Weyl fluids

We theoretically study the single particle Green function of a three dimensional disordered Weyl semimetal using a combination of techniques. These include analytic $T$-matrix and renormalization group methods with complementary regimes of validity, and an exact numerical approach based on the kernel polynomial technique. We show that at any nonzero disorder, Weyl excitations are not ballistic: they instead have a nonzero linewidth that for weak short-range disorder arises from non-perturbative resonant impurity scattering. Perturbative approaches find a quantum critical point between a semimetal and a metal at a finite disorder strength, but this transition is avoided due to nonperturbative effects. At moderate disorder strength and intermediate energies the avoided quantum critical point renormalizes the scaling of single particle properties. In this regime we compute numerically the anomalous dimension of the fermion field and find $\eta= 0.13 \pm 0.04$, which agrees well with a renormalization group analysis ($\eta= 0.125$). Our predictions can be directly tested by ARPES and STM measurements in samples dominated by neutral impurities.

Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization

In quantum Hall edge states and in other one-dimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. If the original charge pulse has some spatial width due to injection with a given source-drain voltage, a finite time is needed until the separation between the fractionalized pulses is larger than their width. In the formalism of non-equilibrium bosonization, the above physics is reflected in the separation of initially overlapping square pulses in the effective scattering phase. When expressing the single particle Green's function as a functional determinant of counting operators containing the scattering phase, the time evolution of charge fractionalization is mathematically described by functional determinants with overlapping pulses. We develop a framework for the evaluation of such determinants, describe the system's equilibration dynamics, and compare our theoretical results with recent experimental findings.

Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent

We show that exact time dependent single particle Green function in the Imambekov–Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlevé IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy–Widom result connecting the Airy kernel with Painlevé II. The asymptotic power law of the exact solution as a function of a single scaling variable x/\sqrt{t}x/t agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.

Effect of external magnetic field on the coexistence of superconductivity and JT distortion in iron pnictides

Abstract We have presented a theoretical study for the coexistence of superconductivity (SC) and Jahn–Teller (JT) effect with applied magnetic field on iron based high- T c superconductors in s -wave symmetry. The analytic expressions for the temperature dependence of the SC and JT order parameters are derived by Zubarev's technique of double time single particle Green's function method and solved self-consistently. It is observed that in the interplay region, both the gap parameters exhibit very strong dependence of their gap values. The effect of external magnetic field on the gap parameters and the electronic density of states (DOS) is studied.

Theory of dielectric loss in Graphene-on-substrate: A tight- binding model study

Graphene-on-substrate exhibits interesting dielectric behaviour due to screening of coulomb interaction induced by many body effects. In this communication we attempt to study the dielectric loss property of graphene within tight-binding model approach. The Hamiltonian consisting of electron hopping upto third-nearest-neighbour's with impurities in two in equivalent sub-lattices. The graphene-on-substrate raises the energy +Δ at one sub lattice and reduces energy -Δ at other sub lattice. Further we introduced coulomb interaction between π - electrons at the two sub lattices separately with the same effective coulomb interaction. We calculate polarization function Π(q, ω) which is a two particle Green's function arising due to charge-charge correlation by using Zubarev's Green's function technique. Finally we calculate dielectric function of graphene i.e. ε(q, ω) =1+Π(q,ω) at arbitrary wave vector q and frequency ra. The dielectric loss in graphene calculated from the imaginary part of dielectric function which is a measure of absorption spectrum. Only a few Fragmentary theoretical attempts have been made to utilize the full frequency and wave vector dependent dielectric function. We compute numerically the frequency dependent dielectric loss function for 100x100 momentum grid points. We observe a low energy Plasmon resonance peak and a high energy flat peak arising due to absorption of optical energy at substrate induced gap. With increase of small Plasmon wave vector, both low and high energy peaks approach each other. The dielectric loss at low energies exhibits a parabolic curve, but it exhibit a clear peak on introduction of higher order electron hopping's. The Coulomb interaction suppresses induced gap in graphene and decreases the optical energy absorption spectra. The increase of substrate induced gap shifts the high energy flat peak to higher energies and enhances the dielectric loss throughout the frequency range. Finally the effect of doping on dielectric loss is investigated and compared with the experimental results.