Analytical approximation for single-impurity Anderson model

We have applied the recently developed dual fermion technique to the spectral properties of single-band Anderson impurity problem (SIAM). In our approach a series expansion is constructed in vertices of the corresponding atomic Hamiltonian problem. This expansion contains a small parameter in two limiting cases: in the weak coupling case ($U/t \to 0$), due to the smallness of the irreducible vertices, and near the atomic limit ($U/t \to \infty$), when bare propagators are small. Reasonable results are obtained also for the most interesting case of strong correlations ($U \approx t$). The atomic problem of the Anderson impurity model has a degenerate ground state, so the application of the perturbation theory is not straightforward. We construct a special approach dealing with symmetry-broken ground state of the renormalized atomic problem. Formulae for the first-order dual diagram correction are obtained analytically in the real-time domain. Most of the Kondo-physics is reproduced: logarithmic contributions to the self energy arise, Kondo-like peak at the Fermi level appears, and the Friedel sum rule is fulfilled. Our approach describes also renormalization of atomic resonances due to hybridization with a conduction band. A generalization of the proposed scheme to a multi-orbital case can be important for the realistic description of correlated solids.Comment: 6 pages, 5 figure

Classical modelling of a bosonic sampler with photon collisions

When the problem of boson sampling was first proposed, it was assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e. the number of photons $M$ injected into the circuit is close to the number of detectors $N$. Here we present a classical algorithm that simulates a bosonic sampler: it calculates the probability of a given photon distribution at the interferometer outputs for a given distribution at the inputs. This algorithm is most effective in cases with multiple photon collisions, and in those cases it outperforms known algorithms

Correlated adatom trimer on metal surface: A continuous time quantum Monte Carlo study

The problem of three interacting Kondo impurities is solved within a numerically exact continuous time quantum Monte Carlo scheme. A suppression of the Kondo resonance by interatomic exchange interactions for different cluster geometries is investigated. It is shown that a drastic difference between the Heisenberg and Ising cases appears for antiferromagnetically coupled adatoms. The effects of magnetic frustrations in the adatom trimer are investigated, and possible connections with available experimental data are discussed.Comment: 4 pages, 4 figure

Electron energy spectrum of the spin-liquid state in a frustrated Hubbard model

Non-local correlation effects in the half-filled Hubbard model on an isotropic triangular lattice are studied within a spin polarized extension of the dual fermion approach. A competition between the antiferromagnetic non-collinear and the spin liquid states is strongly enhanced by an incorporation of a k-dependent self-energy beyond the local dynamical mean-field theory. The dual fermion correc- tions drastically decrease the energy of a spin liquid state while leaving the non-collinear magnetic states almost non-affected. This makes the spin liquid to become a preferable state in a certain interval of interaction strength of an order of the magnitude of a bandwidth. The spectral function of the spin-liquid Mott insulator is determined by a formation of local singlets which results in the energy gap of about twice larger than that of the 120 degrees antiferromagnetic Neel state.Comment: 6 pages, 4 figure

Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include non-local dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical $\sqrt{q}$-behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.Comment: 5 pages, 5 figures + appendix (3 pages, 1 figure

Superperturbation solver for quantum impurity models

We present a very efficient solver for the general Anderson impurity problem. It is based on the perturbation around a solution obtained from exact diagonalization using a small number of bath sites. We formulate a perturbation theory which is valid for both weak and strong coupling and interpolates between these limits. Good agreement with numerically exact quantum Monte-Carlo results is found for a single bath site over a wide range of parameters. In particular, the Kondo resonance in the intermediate coupling regime is well reproduced for a single bath site and the lowest order correction. The method is particularly suited for low temperatures and alleviates analytical continuation of imaginary time data due to the absence of statistical noise compared to quantum Monte-Carlo impurity solvers.Comment: 6 pages, 5 figure

Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems

We propose an efficient dual boson scheme, which extends the DMFT paradigm to collective excitations in correlated systems. The theory is fully self-consistent both on the one- and on the two-particle level, thus describing the formation of collective modes as well as the renormalization of electronic and bosonic spectra on equal footing. The method employs an effective impurity model comprising both fermionic and bosonic hybridization functions. Only single- and two-electron Green's functions of the reference problem enter the theory, due to the optimal choice of the self-consistency condition for the effective bosonic bath. We show that the theory is naturally described by a dual Luttinger-Ward functional and obeys the relevant conservation laws.Comment: 17 pages, 12 figure

Compatible Poisson-Lie structures on the loop group of SL2SL_{2}

We define a 1-parameter family of $r$-matrices on the loop algebra of $sl_{2}$, defining compatible Poisson structures on the associated loop group, which degenerate into the rational and trigonometric structures, and study the Manin triples associated to them.Comment: 5 pages, amstex, no figure