Two-particle Response Functions Research Articles

Ground-state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model

We present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value ${g}_{\mathrm{c}}$. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.

Efficient Slave-Boson Approach for Multiorbital Two-Particle Response Functions and Superconductivity

We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on fluctuation around rotationally-invariant slave-boson saddle-point. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hund's metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels, we identify the mechanism leading to the pairing instability around Hund's metal crossover arises from the particle-particle channel, containing the local electron pair fluctuation between different particle-number sectors of the atomic Hilbert space. On the other hand, the particle-hole spin fluctuations induce the s-wave pairing instability before entering the Hund's regime. Our approach paves the way for investigating the pairing mechanism in realistic correlated materials.

Dynamical response and competing orders in two-band Hubbard model

We present a dynamical mean-field study of two-particle dynamical response functions in two-band Hubbard model across several phase transitions. We observe that the transition between theexcitonic condensate and spin-state ordered state is continuous with a narrow strip of supersolidphase separating the two. Approaching transition from the excitonic condensate is announced bysoftening of the excitonic mode at theMpoint of the Brillouin zone. Inside the spin-state orderedphase there is a magnetically ordered state with 2x2 periodicity, which has no precursor in thenormal phase.

The frozen nucleon approximation in two-particle two-hole response functions

We present a fast and efficient method to compute the inclusive two-particle two-hole (2p–2h) electroweak responses in the neutrino and electron quasielastic inclusive cross sections. The method is based on two approximations. The first neglects the motion of the two initial nucleons below the Fermi momentum, which are considered to be at rest. This approximation, which is reasonable for high values of the momentum transfer, turns out also to be quite good for moderate values of the momentum transfer q≳kF. The second approximation involves using in the “frozen” meson-exchange currents (MEC) an effective Δ-propagator averaged over the Fermi sea. Within the resulting “frozen nucleon approximation”, the inclusive 2p–2h responses are accurately calculated with only a one-dimensional integral over the emission angle of one of the final nucleons, thus drastically simplifying the calculation and reducing the computational time. The latter makes this method especially well-suited for implementation in Monte Carlo neutrino event generators.

Exact response functions within the time-dependent Gutzwiller approach

We investigate the applicability of the two existing versions of a time-dependent Gutzwiller approach (TDGA) beyond the frequently used limit of infinite spatial dimensions. To this end, we study the two-particle response functions of a two-site Hubbard model where we can compare the exact results and those derived from the TDGA. It turns out that only the more recently introduced version of the TDGA can be combined with a diagrammatic approach which allows for the evaluation of Gutzwiller wave functions in finite dimensions. For this TDGA method, we derive the time-dependent Lagrangian for general single-band Hubbard models.

Two-Particle Response in Cluster Dynamical Mean-Field Theory: Formalism and Application to the Raman Response of High-Temperature Superconductors

A method is presented for the unbiased numerical computation of two-particle response functions of correlated electron materials via a solution of the dynamical mean-field equations in the presence of a perturbing field. The power of the method is demonstrated via a computation of the Raman B(1g) and B(2g) scattering intensities of the two-dimensional Hubbard model in parameter regimes believed to be relevant to high-temperature superconductivity. The theory reproduces the "two-magnon" peak characteristic of the Raman intensity of insulating parent compounds of high-T(c) copper oxide superconductors, and shows how it evolves to a quasiparticle response, as carriers are added. The method can be applied in any situation where a solution of equilibrium dynamical mean-field equations is feasible.

Competing orders in NaxCoO2from strong correlations on a two-particle level

Based on dynamical mean-field theory with a continuous-time quantum Monte-Carlo impurity solver, static as well as dynamic spin and charge susceptibilites for the phase diagram of the sodium cobaltate system Na$_x$CoO$_2$ are discussed. The approach includes important vertex contributions to the q-dependent two-particle response functions by means of a local approximation to the irreducible vertex function in the particle-hole channel. A single-band Hubbard model suffices to reveal several charge- and spin-instability tendencies in accordance with experiment, including the stabilization of an effective kagome sublattice close to x=0.67, without invoking the doping-dependent Na-potential landscape. The in-plane antiferromagnetic-to-ferromagnetic crossover is additionally verified by means of the computed Korringa ratio. Moreover an intricate high-energy mode in the transverse spin susceptiblity is revealed, pointing towards a strong energy dependence of the effective intersite exchange.

Time-dependent Gutzwiller theory for multi-band Hubbard models

We formulate a multi-band generalization of the time-dependent Gutzwiller theory. This approach allows for the calculation of general two-particle response functions, which are crucial for an understanding of various experiments in solid-state physics. As a first application, we study the momentum- and frequency-resolved magnetic susceptibility in a two-band Hubbard model. As in the case of underlying ground-state approaches, we find significant differences between the results of our method and those from a time-dependent Hartree–Fock approximation.

Efficient treatment of two-particle vertices in dynamical mean-field theory

We present an efficient and numerically stable algorithm for calculation of two-particle response functions within the dynamical mean-field theory. The technique is based on inferring the high frequency asymptotic behavior of the irreducible vertex function from the local dynamical susceptibility. The algorithm is tested on several examples. In all cases rapid convergence of the vertex function towards its asymptotic form is observed.

Two-particle dynamics in a Luttinger liquid

We study the two-particle dynamics in one-dimensional (1D) electron systems described by the Tomonaga-Luttinger model. By using bosonization methods we compute analytically two different kinds of two-particle response functions. In the first case the creation of the two particles does not involve any other degree of freedom in the system, and the subsequent propagation is described by a standard two-body Green's function. This is relevant to address, e.g, the behavior of recently observed local pairs in 1D optical lattices. In the second case the creation of the two particles occurs coherently with the decay of a third localized particle. Such a condition is crucial to study the Auger transitions in 1D systems like carbon nanotubes, where two holes are left in the valence band after the decay of a core-hole.

Dynamical-quantum-cluster approach to two-particle correlation functions in the Hubbard model

We investigate the charge- and spin-dynamical structure factors for the two-dimensional one-band Hubbard model in the strong coupling regime within the dynamical cluster approximation (DCA) that is explicitly extended to two-particle response functions. The full irreducible two-particle vertex with three momenta and frequencies is approximated by an effective vertex dependent on the momentum and frequency of the spin and/or charge excitation. In the spirit of the DCA, the effective vertex is calculated by using the quantum Monte Carlo methods on a finite cluster. On the basis of a comparison to high temperature auxiliary field quantum Monte Carlo data, we show that near and beyond optimal doping, our results provide a consistent overall picture of the interplay between charge, spin, and single-particle excitations.

Colloidal dynamics in polymer solutions: optical two-point microrheology measurements.

We present an extension of the two-point optical microrheology technique introduced by Crocker et al. [J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh and D. A.Weitz, Phys. Rev. Lett., 2000, 85, 888] to high frequencies. The correlated fluctuations of two probe spheres held by a pair of optical tweezers within a viscoelastic medium are determined using optical interferometry. A theoretical model is developed to yield the frequency-dependent one- and two-particle response functions from the correlated motion. We demonstrate the validity of this method by determining the one- and two-particle correlations in a semi-dilute solution of polystyrene in decalin. We find that the ratio of the one- and two-particle response functions is anomalous which we interpret as evidence for a slip boundary condition caused by depletion of polymer from the surface of the particle.

Superconductivity in the two-dimensional Hubbard model: One-particle correlation functions.

The one-particle correlation functions of a ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ superconducting state in the two-dimensional Hubbard model are investigated within the fluctuation-exchange approximation. This approximation has been previously applied to investigate properties of the Hubbard-model normal state, including incipient instabilities. Results are obtained for the wave vector and temperature dependence of the one-particle energy gap. A miximum gap ratio 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{k}}^{\mathrm{max}}$(T=0)/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$ of order 10 is obtained for intermediate coupling strengths and electron densities near one per site. The potential appearance of spin excitons in two-particle response functions is discussed.

Two-particle spectra of heavy-fermion systems.

Abstract Appearance potential spectra of heavy fermion systems are presented and analyzed in the frame of the Gunnarsson-Schonhammer approach for the Anderson-Impurity model. This procedure has been used successfully to describe a wide variety of one-particle spectroscopies of 4f systems. Here we present a generalization of the Gunnarsson-Schonhammmer approach for two-particle response functions, measured in appearance-potential spectroscopy. Calculations and experiments are presented for CeNi 5 and CePd 3 . It appears that the first term in the 1/N expansion already gives strikingly good agreement with the experimental data and the Gunnarsson-Schonhammer approach describes two-particle response functions as reliably as those of one-particle spectra.

Two-particle spectra of heavy fermion systems

Appearance potential spectra of heavy fermion systems are presented and analyzed in the frame of the Gunnarsson-Schönhammer approach for the Anderson-Impurity model. This procedure has been used successfully to describe a wide variety of one-particle spectroscopies of 4f systems. Here we present a generalization of the Gunnarsson-Schönhammmer approach for two-particle response functions, measured in appearance-potential spectroscopy. Calculations and experiments are presented for CeNi 5 and CePd 3 . It appears that the first term in the 1/N expansion already gives strikingly good agreement with the experimental data and the Gunnarsson-Schönhammer approach describes two-particle response functions as reliably as those of one-particle spectra.

Gauge-invariant response functions of fermions coupled to a gauge field.

We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be cancelled by those from the vertex correction for small $q$ and $\Omega$. As a result, the remaining contributions are not singular enough to change the leading order results of the random phase approximation. It is also shown that the gauge field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small $q$ and $\Omega$, but for all ratios of $\Omega / v_F q$ and we conclude that they can be described by Fermi liquid forms without a diverging effective mass.

Motion of a particle in a Fermi sea: One dimension.

We study the motion of a particle in a degenerate Fermi sea in one dimension by calculating numerically the one-particle spectral function as well as a number of two-particle response functions. The problem is formulated in terms of the eigenstates of the static case, in which the particle is localized at a particular site. In spite of the Anderson orthogonality catastrophe, accurate results for small systems (up to 100 sites and electrons) are obtained with relatively few basis states, i.e., 0 and 1 particle-hole pair excitations. The mobile particle in one dimension does not display ``quasiparticle'' behavior, and most response functions show power-law threshold behavior as in the case of a localized particle, in complete agreement with exact results. We discuss practical applications to optical spectra and to the dynamical mobility of optically generated holes in doped semiconductor quantum wires.

Response behavior of the two-chain Fermi gas

We consider a model of TTF-TCNQ (tetrahiafulvalenium-tetracyanoquinodimethanide) and similar charge-transfer linear conductors in which there are two chains. The electrons on the acceptor (TCNQ) chains have a usual metallic band, but the electrons on the donor (TTF) chains have an inverted or hole band. The electrons on each chain interact via the forward and backward scattering ${g}_{2}$ and ${g}_{1}$ processes, respectively. Electrons on different chains interact via the analogous processes ${W}_{2}$ and ${W}_{1}$. The model is also applicable to two metallic chains, with the signs of ${W}_{1}$ and ${W}_{2}$ reversed. Using the techniques of Luther and Emery and of Chui and Lee we show that the problem may be mapped onto a similar problem of three coupled classical two-dimensional Coulomb gases. In addition to gaps in the spin degrees of freedom that were present in the single-chain problem, we find that the antisymmetric form of the resultant charge degrees of freedom may have a gap. We then investigate the predominant two-, four-, six-, and eight-particle response functions and calculate their temperature dependence. In addition to the four divergent two-particle response functions present in the single chain, there is a region for weak interaction strengths in which the $2{k}_{F}$ interchain Cooper pairing response is the most divergent as $T\ensuremath{\rightarrow}0$. The excitonic insulator response may also be important at high temperatures. For the single chain, either the $4{k}_{F}$ response or a four-particle $q=0$ response is the most divergent for strong coupling and repulsive ${g}_{1}$, depending upon the sign of ${g}_{2}\ensuremath{-}\frac{1}{2}{g}_{1}$. For the two-chain system, the most divergent response as $T\ensuremath{\rightarrow}0$ for strongly attractive interactions (${g}_{1}$ and ${g}_{2}$) is the response to the formation of excitonic molecules or exciton pairs. For strong coupling and repulsive ${g}_{1}$ either $8{k}_{F}$ or octet responses may be observable. We discuss these results in conjunction with our previous renormalization-group treatment, which indicates that for certain values of ${g}_{2}$, ${W}_{2}$, and ${W}_{1}$ the line ${g}_{1}=0$ may be crossed. We use these results to interpret the recent x-ray data on TTF-TCNQ showing a crossover from $4{k}_{F}$ to $2{k}_{F}$ behavior above the crossover from one-dimensional to three-dimensional behavior.