A. N. Rubtsov

Continuous-time quantum Monte Carlo method for fermions

We present a numerically exact continuous-time quantum Monte Carlo algorithm for fermions with a general interaction nonlocal in space-time. The new determinantal grand-canonical scheme is based on a stochastic series expansion for the partition function in the interaction representation. The method is particularly applicable for multiband, time-dependent correlations since it does not invoke the Hubbard-Stratonovich transformation. The test calculations for exactly solvable models, as well results for the Green function and for the time-dependent susceptibility of the multiband supersymmetric model with a spin-flip interaction are discussed.

dc-electric-field-induced and low-frequency electromodulation second-harmonic generation spectroscopy of Si(001)-SiO2 interfaces

The mechanism of dc-electric-field-induced second-harmonic ~EFISH! generation at weakly nonlinear buried Si(001)-SiO2 interfaces is studied experimentally in planar Si(001)-SiO 2-Cr MOS structures by optical second-harmonic generation spectroscopy with a tunable Ti:sapphire femtosecond laser. The spectral dependence of the EFISH contribution near the direct two-photon E1 transition of silicon is extracted. A systematic phenomenological model of the EFISH phenomenon, including a detailed description of the space-charge region ~SCR! at the semiconductor-dielectric interface in accumulation, depletion, and inversion regimes, has been developed. The influence of surface quantization effects, interface states, charge traps in the oxide layer, doping concentration, and oxide thickness on nonlocal screening of the dc-electric field and on breaking of inversion symmetry in the SCR is considered. The model describes EFISH generation in the SCR using a Green’s-function formalism which takes into account all retardation and absorption effects of the fundamental and second-harmonic ~SH! waves, and multiple reflection interference in the SiO 2 layer. The optical interference between field-dependent and -independent contributions to the SH field is considered as aninternal homodyne amplifier of the EFISH effects. Good agreement between the phenomenological model and our EFISH spectroscopic results is demonstrated. Finally, low-frequency electromodulated EFISH is demonstrated as a useful differential spectroscopic technique for studies of the Si-SiO 2 interface in silicon-based metaloxide-semiconductor structures. @S0163-1829~99!01836-6#

Second-harmonic generation in metal and semiconductor low-dimensional structures

Abstract In this article previous and recent results of our nonlinear optical studies of low-dimensional structures are surveyed. Size effect in the optical second-harmonic generation (SHG) from Ag nanocrystals in island films and CdSe quantum dots in glass matrices as well as thermo- and DC-electric-field-induced effects in SHG from SiSiO2 multiple quantum wells (MQWs) on Si substrate are studied experimentally and theoretically. Essential (by several orders of magnitude) enhancement of quadratic optical response upon decrease in the particle size is observed for both Ag nanocrystals and CdSe quantum dots. Regular oscillations in the second-harmonic intensity measured as functions of temperature and applied DC electric field are observed for MQWs. It is shown that the size effect for metal nanocrystals can result from the fluctuations of the particle size breaking the local inversion symmetry. Another mechanism studied (based on concepts of dynamic chaos) describes the observed size effects for both metal and semiconductor particles. The dependence of the second-harmonic intensity on the SiO2 layer thickness in MQWs is described with taking into account the retardation of the second-harmonic radiation in MQWs, whereas the thermoinduced effect is interpreted as resulting from the optical interference in the MQWs substrate having thickness dependent on temperature (due to the thermal expansion). A possible approach to explaining the observed electroinduced effect in MQWs is also discussed.

Enhanced crystal-field splitting and orbital-selective coherence induced by strong correlations in V 2 O 3

We present a study of the paramagnetic metallic and insulating phases of vanadium sesquioxide by means of the Nth order muffin-tin orbital implementation of density functional theory combined with dynamical mean-field theory. The transition is shown to be driven by a correlation-induced enhancement of the crystal-field splitting within the t 2g manifold, which results in a suppression of the hybridization between the a 1g and e g π bands. We discuss the changes in the effective quasiparticle band structure caused by the correlations and the corresponding self-energies. At temperatures of about 400 K, we find the a 1g orbital displays coherent quasiparticle behavior, while a large imaginary part of the self-energy and broad features in the spectral function indicate that the e g π orbitals are still far above their coherence temperature. The local spectral functions are in excellent agreement with recent bulk sensitive photoemission data. Finally, we also make a prediction for angle-resolved photoemission experiments by calculating momentum-resolved spectral functions.

Dual fermion approach to the two-dimensional Hubbard model : Antiferromagnetic fluctuations and Fermi arcs

We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-type models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original ones and correspond to weakly interacting quasiparticles in the case of strong local correlations in the Hubbard model. The method starts with dynamical mean-field theory as a zeroth-order approximation and includes nonlocal effects in a perturbative way. In contrast to cluster approaches, this method utilizes an exact transition to a dual set of variables. It therefore becomes possible to treat vertices of an effective single-impurity problem as small parameters. This provides a very efficient interpolation between bandlike weak-coupling and atomic limits. The method is illustrated on the two-dimensional Hubbard model. The antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects due to the Van Hove singularity are correctly reproduced by the lowest-order diagrams. Extremum properties of the dual fermion approach are discussed in terms of the Feynman variational principle.

Efficient Perturbation Theory for Quantum Lattice Models

We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.

Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem

When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.

Dual boson approach to collective excitations in correlated fermionic systems

Abstract We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.

Continuous-time quantum Monte Carlo method for fermions: Beyond auxiliary field framework

A numerically exact continuous-time quantum Monte Carlo algorithm for finite fermionic systems with nonlocal interactions is proposed. The scheme is particularly applicable for general multiband time-dependent correlations, since it does not invoke Hubbard-Stratonovich transformation. The present determinantal grand-canonical method is based on a stochastic series expansion for the partition function in the interaction representation. The results for the Green function and for the time-dependent susceptibility of multiorbital supersymmetric impurity model with a spin-flip interaction are presented.

Dynamical screening effects in correlated materials: Plasmon satellites and spectral weight transfers from a Green's function ansatz to extended dynamical mean field theory

Dynamical screening of the Coulomb interactions in correlated electron systems results in a low-energy effective problem with a dynamical Hubbard interaction U(omega). We propose a Greens function ansatz for the Anderson impurity problem with retarded interactions, in which the Greens function factorizes into a contribution stemming from an effective static-U problem and a bosonic high-energy part introducing collective plasmon excitations. Our approach relies on the scale separation of the low-energy properties, related to the instantaneous static U, from the intermediate to high energy features originating from the retarded part of the interaction. We argue that for correlated materials where retarded interactions arise from downfolding higher-energy degrees of freedom, the characteristic frequencies are typically in the antiadiabatic regime. In this case, accurate approximations to the bosonic factor are relatively easy to construct, with the most simple being the boson factor of the dynamical atomic limit problem. We benchmark the quality of our method against numerically exact continuous time quantum Monte Carlo results for the Anderson-Holstein model both, at half- and quarter-filling. Furthermore we study the Mott transition within the Hubbard-Holstein model within extended dynamical mean field theory. Finally, we apply our technique to a realistic three-band Hamiltonian for SrVO3. We show that our approach reproduces both, the effective mass renormalization and the position of the lower Hubbard band by means of a dynamically screened U, previously determined ab initio within the constrained random phase approximation. Our approach could also be used within schemes beyond dynamical mean field theory, opening a quite general way of describing satellites and plasmon excitations in correlated materials.