Current-current Correlation Function Research Articles

Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations.

Numerically "exact" methods addressing the dynamics of coupled electron-phonon systems have been intensively developed. Nevertheless, the corresponding results for the electron mobility μdc are scarce, even for the one-dimensional (1d) Holstein model. Building on our recent progress on single-particle properties, here we develop the momentum-space hierarchical equations of motion (HEOM) method to evaluate real-time two-particle correlation functions of the 1d Holstein model at a finite temperature. We compute numerically "exact" dynamics of the current-current correlation function up to real times sufficiently long to capture the electron's diffusive motion and provide reliable results for μdc in a wide range of model parameters. In contrast to the smooth ballistic-to-diffusive crossover in the weak-coupling regime, we observe a temporally limited slow-down of the electron on intermediate time scales already in the intermediate-coupling regime, which translates to a finite-frequency peak in the optical response. Our momentum-space formulation lowers the numerical effort with respect to existing HEOM-method implementations, while we remove the numerical instabilities inherent to the undamped-mode HEOM by devising an appropriate hierarchy closing scheme. Still, our HEOM remains unstable at too low temperatures, for too strong electron-phonon coupling, and for too fast phonons.

ACFlow: An open source toolkit for analytic continuation of quantum Monte Carlo data

The purpose of analytic continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, spin and charge susceptibilities) from noisy data generated in finite temperature quantum Monte Carlo simulations. It requires numerical solutions of a family of Fredholm integral equations of the first kind, which is indeed a challenging task. In this paper, an open source toolkit (dubbed ACFlow) for analytic continuation of quantum Monte Carlo data is presented. We first give a short introduction to the analytic continuation problem. Next, three popular analytic continuation algorithms, including the maximum entropy method, the stochastic analytic continuation, and the stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate on the major features, implementation details, basic usage, inputs, and outputs of this toolkit. Finally, four representative examples, including analytic continuations of Matsubara self-energy function, Matsubara and imaginary time Green's functions, and current-current correlation function, are shown to demonstrate the usefulness and flexibility of the ACFlow toolkit. Program summaryProgram Title: ACFlowCPC Library link to program files:https://doi.org/10.17632/th6w74gwjm.1Developer's repository link:https://github.com/huangli712/ACFlowLicensing provisions: GNU General Public License Version 3Programming language: JuliaNature of problem: Most of the quantum Monte Carlo methods work on imaginary axis. In order to extract physical observables and compare them with the experimental results, analytic continuation must be done in the post-processing stage to convert the quantum Monte Carlo simulated data from imaginary axis to real axis.Solution method: Three well-established analytic continuation methods, including the maximum entropy method, the stochastic analytic continuation (both A. W. Sandvik's and K. S. D. Beach's algorithms), and the stochastic optimization method, have been implemented in the ACFlow toolkit.Additional comments including restrictions and unusual features: The ACFlow toolkit is written in pure Julia language. It is highly optimized and parallelized. It can be executed interactively in a Jupyter notebook environment.

Low-energy excitations and transport functions of the one-dimensional Kondo insulator

Using variational matrix product states, we analyze the finite temperature behavior of a half-filled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of single-particle Green’s functions, two-particle Green’s functions, and transport functions creating a broad picture of the low-temperature properties. We confirm the existence of energetically low-lying spin excitations in this model and study their energy-momentum dispersion and temperature dependence. We demonstrate that charge-charge correlations at the Fermi energy exhibit a different temperature dependence than spin-spin correlations. While energetically low-lying spin excitations emerge approximately at the Kondo temperature, which exponentially depends on the interaction strength, charge correlations vanish already at high temperatures. Furthermore, we analyze the charge and thermal conductivity at finite temperatures by calculating the time-dependent current-current correlation functions. While both charge and thermal conductivity can be fitted for all interaction strengths by gapped systems with a renormalized band gap, the gap in the system describing the thermal conductivity is generally smaller than the system describing the charge conductivity. Thus, two-particle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this one-dimensional Kondo insulator is already decreasing while the heat conductivity is still increasing.

Method for obtaining polaron mobility using real and imaginary time path-integral quantum Monte Carlo

We developed a path-integral quantum Monte Carlo-based methodology for calculation of polaron mobility in systems with electron-phonon interaction. Within the method, the current-current correlation function in both the imaginary and real time is calculated in a numerically exact way. The choice of basis for representation of the path integral enabled us to reduce the sign problem and perform real-time calculations for longer times. The DC polaron mobility was extracted by performing analytic continuation that makes use of both the real and imaginary-time data. The method was applied to the Holstein polaron model in one dimension. We obtained reliable results for the temperature dependence of the Holstein polaron mobility for interactions ranging from weak to strong and temperatures that are not too low.

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. A similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.

Production rate and ellipticity of lepton pairs from a rotating hot and dense QCD medium

Using a current-current correlation function (CF), the photon polarization tensor is calculated for a rotating hot and dense QCD medium. The spectral function (SF) and the dilepton rate (DR) are estimated therefrom. Numerical results show that both SF and DR are enhanced in a rotating medium, especially in a low invariant mass region. SF and DR are also explored in the consequences of the interplay among the angular velocity, temperature and chemical potential. We also estimated the electromagnetic screening by calculating the Debye mass and it shows a suppression for a rotating QCD medium. The most interesting observation is the azimuthal anisotropy of the dilepton production, i.e, the elliptic flow $v_{2}$ of the lepton pair induced by the rotation as an external field. The competition between the centrifugal effect and the spin polarization effect due to rotation results in a convex down behaviour of the elliptic flow as a function of the transverse momentum in a relatively large magnitude of angular velocity. It is noticed that quark spin polarization induces a negative $v_2$ in the case of large angular velocity.

Two-wire junction of inequivalent Tomonaga-Luttinger liquids

We develop two novel numerical schemes to study the conductance of the two-wire junction of inequivalent Tomonaga-Luttinger Liquids. In the first scheme we use the static current-current correlation function across the junction to extract the linear conductance through a relation that is derived via the bosonization method. In the second scheme we apply a bias and evaluate the time-dependent current across the junction to obtain the current-voltage characteristic. The conductance is then extracted from the small bias result within the linear response regime. Both schemes are based on the infinite size matrix product state to minimize the finite-size effects. Due to the lack of the translational invariance, we focus on a finite-size window containing the junction. For time-independent calculations, we use infinite boundary conditions to evaluate the correlations within the window. For time-dependent calculations, we use the window technique to evaluate the local currents within the window. The numerical results obtained by both schemes show excellent agreement with the analytical predictions.

Thermal properties of Dirac fermions in Xenes: Model studies

The thermal properties and the electrical conductance are studied for 2D electron gases in doped Xenes -- graphene, silicene, germanene, stanene, and plumbene -- applying a four-band model to describe the low-energy Dirac-fermion-like electronic excitations. Spin-orbit interactions to discriminate the five Xenes and the influence of an electric field in the normal direction, are taken into account. The density of states and the spectral behavior of the current-current correlation function allow the calculation of the Onsager coefficients. They give analytical formulas for the electronic contributions to the heat capacity and thermal conductance. Also, the electrical conductance can be described within the same framework, if the scattering properties of the electron gases are simulated by constant broadening parameters. For all these thermal and transport properties, only a weak variation with the Xene is found, because of their small spin-orbit-induced gaps, with the exception of plumbene. The heat capacity of Xenes does not show a Schottky anomaly. The thermal conductance increases linearly or quadratically with temperature depending on the temperature range. A similar behavior characterizes the electrical conductance. The dominance of Dirac fermions, i.e., linear bands, determines the ratio of electron thermal conductance and electric conductance, which depends on doping level and temperature. It violates the Wiedemann-Franz law known for 3D electron gases with parabolic energy-momentum dispersion. The Lorenz number is generally much larger for 2D electron gases with almost Dirac character of the dispersion relation.

Momentum-resolved conductivity of strongly interacting bosons in an optical lattice

Motivated by the recent advancements in experimental techniques in the cold atomic systems, we study the dependence of the conductivity on momentum in a system of strongly interacting bosons in an optical lattice. By employing the quantum rotor approach to the Bose-Hubbard model we calculate the current-current correlation function and subsequently obtain the analytic formula for the momentum-dependent longitudinal conductivity. We analyze the behavior of the conductivity for the square and cubic lattices in both, the superfluid and Mott insulator phases. As a consequence of the particle-hole symmetry, the conductivity for a uniformly filled lattice in the superfluid phase exhibits a linear dependence for a surprisingly wide range of momenta around $\mathbf{k}=0$. This allows us to predict the value of the group velocity of the particle excitations. We also consider the impact of finite temperature and discover that it leads to an additional conductivity channel, which is aligned along the direction of the probe field and located within the energy gap.

Comparison of optical response from DFT random phase approximation and a low-energy effective model: Strained phosphorene

The engineering of the optical response of materials is a paradigm that demands microscopic-level accuracy and reliable predictive theoretical tools. Here we compare and contrast the dispersive permittivity tensor, using both a low-energy effective model and density functional theory (DFT). As a representative material, phosphorene subject to strain is considered. Employing a low-energy model Hamiltonian with a Green's function current-current correlation function, we compute the dynamical optical conductivity and its associated permittivity tensor. For the DFT approach, first-principles calculations make use of the first-order random phase approximation. Our results reveal that although the two models are generally in agreement within the low-strain and low-frequency regime, the intricate features associated with the fundamental physical properties of the system and optoelectronics devices implementation such as band gap, Drude absorption response, vanishing real part, absorptivity, and sign of permittivity over the frequency range show significant discrepancies. Our results suggest that the random phase approximation employed in widely used DFT packages should be revisited and improved to be able to predict these fundamental electronic characteristics of a given material with confidence. Furthermore, employing the permittivity results from both models, we uncover the pivotal role that phosphorene can play in optoelectronics devices to facilitate highly programable perfect absorption of electromagnetic waves by manipulating the chemical potential and exerting strain and illustrate how reliable predictions for the dielectric response of a given material are crucial to precise device design.

Towards charged hadron polarizabilities from four-point functions in lattice QCD

We show how to compute electromagnetic polarizabilities of charged hadrons using four-point functions in lattice QCD. The low-energy behavior of Compton scattering amplitude is matched to matrix elements of current-current correlation functions on the lattice. Working in momentum space, formulas for electric polarizability ($\alpha_E$) and magnetic polarizability ($\beta_M$) are derived for both charged pion and proton. Lattice four-point correlation functions are constructed from quark and gluon fields to be used in Monte-Carlo simulations. The content of the functions is assessed in detail and specific prescriptions are given to isolate the polarizabilities. The connected quark-line diagrams can be done today as a small lattice project. The disconnected diagrams are more challenging but are within reach of dedicated resources for medium to large lattice projects. We also draw attention to the potential of four-point functions as a multi-purpose tool for hadron structure.

The Effect of Magnetic Field on Optical Conductivity of Hexagonal Boron-Nitride Sheet

The main purpose of this work is to investigate the effect of external magnetic field on the optical absorption of single-layer hexagonal boron nitride. The optical absorption of the system can be found by calculating the imaginary part of the dielectric function. The optical absorption is proportional to from the real part of the dynamical electrical conductivity function. Based on linear response theory, dynamical conductivity function can be calculated in terms of the current-current correlation function. In this study, the tight-binding model Hamiltonian has been applied to study the electronic band spectrum of the system. Also, the energy spectrum of electrons is calculated in the presence of a magnetic field along perpendicular to the plane. The Green’s function approach has been explored to obtain current-current correlation function and optical conductivity. The results show applying magnetic field has significant effects on dependence of optical absorption of boron nitride system on photon frequency and temperature.

Running Coupling Constant from Position-Space Current-Current Correlation Functions in Three-Flavor Lattice QCD.

In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), α_{s}^{MS[over ¯]}(μ), for MS[over ¯] renormalization scales μ∈(1,2) GeV. The computation uses gauge field configuration ensembles with O(a)-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has never been applied before in this context. We convert the results perturbatively to the QCD Λ parameter and obtain Λ_{MS[over ¯]}^{N_{f}=3}=342±17 MeV, which agrees with the world average published by the Particle Data Group and has competing precision. The latter was made possible by a unique combination of state-of-the-art CLS ensembles with very fine lattice spacings, further reduction of discretization effects from a dedicated numerical stochastic perturbation theory simulation, combining data from vector and axial-vector channels, and matching to high-order perturbation theory.

Statistical correlations of currents flowing through a proximized quantum dot

Statistical properties of the electron transport flowing through nanostructures are strongly influenced by the interactions, geometry of the system and/or by type of the external electrodes. These factors affect not only the average current induced in the system but also contribute to fluctuations in the flux of charges and their correlations. Due to possible applications of the hybrid nano-systems, containing one or more superconducting electrodes, a detailed understanding of the flow of charge and its fluctuations seems to be of primary importance. Coulomb repulsion between electrons usually strongly affect the current-current correlation function. In this work we study the correlations in the charge flow through such interacting quantum dot contacted to one superconducting and two normal electrodes. This set-up allows for analysis of the Andreev scattering events in the correlations of currents flowing between external electrodes and, in particular, gives access to cross-correlations between currents from/to different normal electrodes. Our approach relies on the master equation technique, which properly captures the Coulomb interactions. We study the finite frequency correlations and find the relaxation processes, related to the high frequency charge and low frequency polarisation fluctuations. The multiterminal structure of here studied single electron device allows to analyze a competition between the intra- and inter-channel correlations. In the appropriate limit of the interacting quantum dot embedded between two normal electrodes our calculations quantitatively describe the recent experimental data on the frequency dependent correlations. This shows a promising potential of the method for description of the hybrid systems with superconducting electrode(s).

Effective model for the A2g Raman signal in URu2Si2

We propose an effective model to describe the $A_{2g}$ signal in Raman scattering experiments in the URu$_{2}$Si$_{2}$ compound. We follow the scheme proposed earlier by Khveshchenko and Wiegmann [Phys. Rev. Lett. 73, 500 (1994)] to calculate the $A_{2g}$ scattering vertex. We extract the imaginary part of a two-point current-current correlation function and compare it directly with the Raman response. We obtain an inelastic peak at $A_{2g}$ channel owing to the interplay between a local staggered ordering and a possible quantum spin liquid behavior. Our results offer an explanation for the electronic Raman scattering experiments at the hidden order phase in URu$_{2}$Si$_{2}$ compound [Phys. Rev. Lett. 113, 266405 (2014)].

Current-current deformations, conformal integrals and correlation functions

Motivated by the recent work on Toverline{T} -type deformations of 2D CFTs, a especial class of single-trace deformations of AdS3/CFT2 correspondence has been investigated. From the worldsheet perspective, this corresponds to a marginal deformation of the σ - model on AdS3 that yields a string background that interpolates between AdS3 and a flat linear dilaton solution. Here, with the intention of studying this worldsheet CFT further, we consider it in the presence of a boundary. In a previous paper, we computed different correlation functions of this theory on the disk, including the bulk 1-point function, the boundary-boundary 2-point function, and the bulk-boundary 2-point function. This led us to compute the anomalous dimension of both bulk and boundary vertex operators, which first required a proper regularization of the ultraviolet divergences of the conformal integrals. Here, we extend the analysis by computing the bulk-bulk 2-point function on the disk and other observables on the sphere. We prove that the renormalization of the vertex operators proposed in our previous works is consistent with the form of the sphere N -point functions.

ORDER, DISORDER AND PHASE TRANSITIONS IN QUANTUM MANY BODY SYSTEMS

In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on the universality of transport coecients in lattice models of interacting electrons, with specic focus on the in- dependence of the quantum Hall conductivity from the electron-electron interaction. In this context, the exchange of ideas between mathematical and theoretical physics proved particu- larly fruitful, and helped in clarifying the role played by quantum conservation laws (Ward Identities), together with the decay properties of the Euclidean current-current correlation functions, on the interaction-independence of the conductivity.

Current correlation functions from a bosonized theory in 3/2+1 dimensions

Within the context of a bosonized theory, we evaluate the current-current correlation functions corresponding to a massive Dirac field in 2+1 dimensions, which is constrained to a spatial half-plane. The boundary conditions are imposed on the dual theory, and have the form of of perfect-conductor conditions. We also consider, for the sake of comparison, the purely fermionic version of the model and its boundary conditions, in the large-mass limit. We apply the result about the dual theory to the evaluation of induced vacuum currents in the presence of an external field, in a spatial half-plane.

QED self-energies from lattice QCD without power-law finite-volume errors

Using the infinite-volume photon propagator, we developed a method which allows us to calculate electromagnetic corrections to stable hadron masses with only exponentially suppressed finite-volume effects. The key idea is that the infinite volume hadronic current-current correlation function with large time separation between the two currents can be reconstructed by its value at modest time separation, which can be evaluated in finite volume with only exponentially suppressed errors. This approach can be extended to other possible applications such as QED corrections to (semi-)leptonic decays and some rare decays.

Response functions of hot and dense matter in the Nambu-Jona-Lasino model * * Supported by the National Natural Science Foundation of China (11775123, 11890712, 11747312, 11475062) and the National Key R&D Program of China (2018YFA0306503)

We investigate current-current correlation functions, or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics, namely mean-field theory and a beyond-mean-field theory, taking into account mesonic contributions. Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation, showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the self-energy or density-of-state contribution, and the Maki-Thompson contribution. Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to carefully treat the linear terms in external sources and the induced perturbations. In the chiral symmetry breaking phase, we find an additional chiral order parameter induced contribution, which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities. These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover, where the mesonic degrees of freedom are still important.