Effects of electron-phonon coupling range on the polaron formation

The polaron features due to electron-phonon interactions with different coupling ranges are investigated by adopting a variational approach. The ground-state energy, the spectral weight, the average kinetic energy, the mean number of phonons, and the electron-lattice correlation function are discussed for the system with coupling to local and nearest neighbor lattice displacements comparing the results with the long range case. For large values of the coupling with nearest neighbor sites, most physical quantities show a strong resemblance with those obtained for the long range electron-phonon interaction. Moreover, for intermediate values of interaction strength, the correlation function between electron and nearest neighbor lattice displacements is characterized by an upturn as function of the electron-phonon coupling constant.Comment: 5 pages and 4 figure

A cellular automaton for the factor of safety field in landslides modeling

Landslide inventories show that the statistical distribution of the area of recorded events is well described by a power law over a range of decades. To understand these distributions, we consider a cellular automaton to model a time and position dependent factor of safety. The model is able to reproduce the complex structure of landslide distribution, as experimentally reported. In particular, we investigate the role of the rate of change of the system dynamical variables, induced by an external drive, on landslide modeling and its implications on hazard assessment. As the rate is increased, the model has a crossover from a critical regime with power-laws to non power-law behaviors. We suggest that the detection of patterns of correlated domains in monitored regions can be crucial to identify the response of the system to perturbations, i.e., for hazard assessment.Comment: 4 pages, 3 figure

Phase Diagram of the Bose-Hubbard Model with T_3 symmetry

In this paper we study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with T_3 structure, the "dice lattice". Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the T_3 structure. The zero-temperature critical point as a function of a magnetic field shows the characteristic "butterfly" form. At fully frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f=1/2, we find evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the T_3 lattice. We name this new phase the Aharonov-Bohm (AB) insulator. In the presence of charge frustration the phase diagram acquires the typical lobe-structure. The form and hierarchy of the Mott insulating states with fractional fillings, is dictated by the particular topology of the T_3 lattice. The results presented in this paper were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side, and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed Quantum Monte Carlo simulations of the corresponding (2+1)D XY model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the T_3 lattice both with optical lattices and with Josephson junction arrays.Comment: 16 pages, 17 figure

A variational approach to the optimized phonon technique for electron-phonon problems

An optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems is proposed. The variational method is based on an expansion in coherent states that leads to a dramatic truncation in the phonon space. The reliability of the approach is demonstrated for the extended Holstein model showing that different types of lattice distortions are present at intermediate electron-phonon couplings as observed in strongly correlated systems. The connection with the density matrix renormalization group is discussed.Comment: 4 figures; submitted to Phys. Rev.

Interplay of charge, spin and lattice degrees of freedom on the spectral properties of the one-dimensional Hubbard-Holstein model

We calculate the spectral function of the one dimensional Hubbard-Holstein model using the time dependent Density Matrix Renormalization Group (tDMRG), focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple peaks in the spectrum with an energy separation corresponding to the energy of the lattice vibrations (i.e., phonons). We support the numerical results by introducing a well controlled analytical approach based on Ogata-Shiba's factorized wave-function, showing that the spectrum can be understood as a convolution of three contributions, originating from charge, spin, and lattice sectors. We recognize and interpret these signatures in the spectral properties and discuss the experimental implications.Comment: 8 pages, 7 figure

Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Non-Equilibrium: Application to Pump-Probe Phenomena

The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultra short powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a 3-peak structure in agreement with experimental observations. After an ultra short pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the relaxation time of the charge system. We propose a criterion for observing these oscillations in high $T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to be shorter than the phonon oscillation period $T_{ph}$.Comment: 4 pages, 4 figure

Spectral, optical and transport properties of the adiabatic anisotropic Holstein model: Application to slightly doped organic semiconductors

Spectral, optical and transport properties of an anisotropic three-dimensional Holstein model are studied within the adiabatic approximation. The parameter regime is appropriate for organic semiconductors used in single crystal based field effect transistors. Different approaches have been used to solve the model: self-consistent Born approximation valid for weak electron-phonon coupling, coherent potential approximation exact for infinite dimensions, and numerical diagonalization for finite lattices. With increasing temperature, the width of the spectral functions gets larger and larger making the approximation of quasi-particle less accurate. On the contrary, their peak positions are never strongly renormalized in comparison with the bare ones. As expected, the density of states is characterized by an exponential tail corresponding to localized states at low temperature. For weak electron-lattice coupling, the optical conductivity follows a Drude behavior, while, for intermediate electron-lattice coupling, a temperature dependent peak is present at low frequency. For high temperatures and low particle densities, the mobility always exhibits a power-law behavior as function of temperature. With decreasing the particle density, at low temperature, the mobility shows a transition from metallic to insulating behavior. Results are discussed in connection with available experimental data.Comment: 9 pages, 7 figures, submitted to Phys. Rev.

Electronic transport within a quasi two-dimensional model for rubrene single-crystal field effect transistors

Spectral and transport properties of the quasi two-dimensional adiabatic Su-Schrieffer-Heeger model are studied adjusting the parameters in order to model rubrene single-crystal field effect transistors with small but finite density of injected charge carriers. We show that, with increasing temperature $T$, the chemical potential moves into the tail of the density of states corresponding to localized states, but this is not enough to drive the system into an insulating state. The mobility along different crystallographic directions is calculated including vertex corrections which give rise to a transport lifetime one order of magnitude smaller than spectral lifetime of the states involved in the transport mechanism. With increasing temperature, the transport properties reach the Ioffe-Regel limit which is ascribed to less and less appreciable contribution of itinerant states to the conduction process. The model provides features of the mobility in close agreement with experiments: right order of magnitude, scaling as a power law $T^{-\gamma}$, with $\gamma$ close or larger than two, and correct anisotropy ratio between different in-plane directions. Due to a realistic high dimensional model, the results are not biased by uncontrolled approximations.Comment: 10 pages, 9 figures, Submitte

Rashba effect induced localization in quantum networks

We study a quantum network extending in one-dimension (chain of square loops connected at one vertex) made up of quantum wires with Rashba spin-orbit coupling. We show that the Rashba effect may give rise to an electron localization phenomenon similar to the one induced by magnetic field. This localization effect can be attributed to the spin precession due to the Rashba effect. We present results both for the spectral properties of the infinite chain, and for linear transport through a finite-size chain connected to leads. Furthermore, we study the effect of disorder on the transport properties of this network.Comment: To appear in Phys. Rev. Let

4e-condensation in a fully frustrated Josephson junction diamond chain

Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\c{c}ot and J. Vidal, Phys. Rev. Lett. {\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.Comment: 5 pages, 7 figure