Can model Hamiltonians describe the electron–electron interaction in π-conjugated systems?: PAH and graphene

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser–Parr–Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree–Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree–Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an 'effective' Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Modelling the Sun's small scale global photospheric magnetic field

We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small- scale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms, to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between small-scale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2:5 Rʘ, around 10 - 100 times less than that determined for typical HMI synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is presently observed, and hence a much higher cosmic ray flux at Earth.

High-temperature superconductivity in the two-dimensional t-J model: Gutzwiller wavefunction solution

A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t-J model with the hopping electron amplitudes t (and t') between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the method's results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed 'grand-canonical Gutzwiller approximation' (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a d(x2-y2) wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the

Origin of primordial magnetic fields

Magnetic fields of intensities similar to those in our galaxy are also observed in high redshift galaxies, where a mean field dynamo would not have had time to produce them. Therefore, a primordial origin is indicated. It has been suggested that magnetic fields were created at various primordial eras: during inflation, the electroweak phase transition, the quark-hadron phase transition (QHPT), during the formation of the first objects, and during reionization. We suggest here that the large-scale fields similar to mu G, observed in galaxies at both high and low redshifts by Faraday rotation measurements (FRMs), have their origin in the electromagnetic fluctuations that naturally occurred in the dense hot plasma that existed just after the QHPT. We evolve the predicted fields to the present time. The size of the region containing a coherent magnetic field increased due to the fusion of smaller regions. Magnetic fields (MFs) similar to 10 mu G over a comoving similar to 1 pc region are predicted at redshift z similar to 10. These fields are orders of magnitude greater than those predicted in previous scenarios for creating primordial magnetic fields. Line-of-sight average MFs similar to 10(-2) mu G, valid for FRMs, are obtained over a 1 Mpc comoving region at the redshift z similar to 10. In the collapse to a galaxy (comoving size similar to 30 kpc) at z similar to 10, the fields are amplified to similar to 10 mu G. This indicates that the MFs created immediately after the QHPT (10(-4) s), predicted by the fluctuation-dissipation theorem, could be the origin of the similar to mu G fields observed by FRMs in galaxies at both high and low redshifts. Our predicted MFs are shown to be consistent with present observations. We discuss the possibility that the predicted MFs could cause non-negligible deflections of ultrahigh energy cosmic rays and help create the observed isotropic distribution of their incoming directions. We also discuss the importance of the volume average magnetic field predicted by our model in producing the first stars and in reionizing the Universe.

Exotic phases induced by strong spin-orbit coupling in ordered double perovskites

We construct and analyze a microscopic model for insulating rocksalt ordered double perovskites, with the chemical formula A(2)BB'O(6), where the B' atom has a 4d(1) or 5d(1) electronic configuration and forms a face-centered-cubic lattice. The combination of the triply degenerate t(2g) orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment j=3/2. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to three main phases: an unusual antiferromagnet with dominant octupolar order, a ferromagnetic phase with magnetization along the [110] direction, and a nonmagnetic but quadrupolar ordered phase, which is stabilized by thermal fluctuations and intermediate temperatures. All these phases have a two-sublattice structure described by the ordering wave vector Q=2 pi(001). We consider quantum fluctuations and argue that in the regime of dominant antiferromagnetic exchange, a nonmagnetic valence-bond solid or quantum-spin-liquid state may be favored instead. Candidate quantum-spin-liquid states and their basic properties are described. We also address the effect of single-site anisotropy driven by lattice distortions. Existing and possible future experiments are discussed in light of these results.

Pitfalls driven by the sole use of local updates in dynamical

The recent claim that the exit probability (EP) of a slightly modified version of the Sznadj model is a continuous function of the initial magnetization is questioned. This result has been obtained analytically and confirmed by Monte Carlo simulations, simultaneously and independently by two different groups (EPL, 82 (2008) 18006; 18007). It stands at odds with an earlier result which yielded a step function for the EP (Europhys. Lett., 70 (2005) 705). The dispute is investigated by proving that the continuous shape of the EP is a direct outcome of a mean-field treatment for the analytical result. As such, it is most likely to be caused by finite-size effects in the simulations. The improbable alternative would be a signature of the irrelevance of fluctuations in this system. Indeed, evidence is provided in support of the stepwise shape as going beyond the mean-field level. These findings yield new insight in the physics of one-dimensional systems with respect to the validity of a true equilibrium state when using solely local update rules. The suitability and the significance to perform numerical simulations in those cases is discussed. To conclude, a great deal of caution is required when applying updates rules to describe any system especially social systems. Copyright (C) EPLA, 2011

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Phonon anomalies due to strong-electronic correlations in layered organic metals

We show how the coupling between the phonons and electrons in a strongly correlated metal can result in phonon frequencies that have a nonmonotonic temperature dependence. Dynamical mean-field theory is used to study the Hubbard-Holstein model that describes the kappa-(BEDT-TTF)(2)X [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] family of superconducting molecular crystals. The crossover with increasing temperature from a Fermi liquid to a bad metal produces phonon anomalies that are relevant to recent Raman scattering and acoustic experiments.

Nonmonotonic Magnetic Susceptibility of Dipolar Hard-Spheres at Low Temperature and Density

We investigate, via numerical simulations, mean field, and density functional theories, the magnetic response of a dipolar hard sphere fluid at low temperatures and densities, in the region of strong association. The proposed parameter-free theory is able to capture both the density and temperature dependence of the ring-chain equilibrium and the contribution to the susceptibility of a chain of generic length. The theory predicts a nonmonotonic temperature dependence of the initial (zero field) magnetic susceptibility, arising from the competition between magnetically inert particle rings and magnetically active chains. Monte Carlo simulation results closely agree with the theoretical findings. DOI: 10.1103/PhysRevLett.110.148306

Learning joint representations for order and timing of perceptual-motor sequences: a dynamic neural field approach

Many of our everyday tasks require the control of the serial order and the timing of component actions. Using the dynamic neural field (DNF) framework, we address the learning of representations that support the performance of precisely time action sequences. In continuation of previous modeling work and robotics implementations, we ask specifically the question how feedback about executed actions might be used by the learning system to fine tune a joint memory representation of the ordinal and the temporal structure which has been initially acquired by observation. The perceptual memory is represented by a self-stabilized, multi-bump activity pattern of neurons encoding instances of a sensory event (e.g., color, position or pitch) which guides sequence learning. The strength of the population representation of each event is a function of elapsed time since sequence onset. We propose and test in simulations a simple learning rule that detects a mismatch between the expected and realized timing of events and adapts the activation strengths in order to compensate for the movement time needed to achieve the desired effect. The simulation results show that the effector-specific memory representation can be robustly recalled. We discuss the impact of the fast, activation-based learning that the DNF framework provides for robotics applications.

The Spread of free-riding behavior in a social network

We study a model where agents, located in a social network, decide whether to exert effort or not in experimenting with a new technology (or acquiring a new skill, innovating, etc.). We assume that agents have strong incentives to free ride on their neighbors' effort decisions. In the static version of the model efforts are chosen simultaneously. In equilibrium, agents exerting effort are never connected with each other and all other agents are connected with at least one agent exerting effort. We propose a mean-field dynamics in which agents choose in each period the best response to the last period's decisions of their neighbors. We characterize the equilibrium of such a dynamics and show how the pattern of free riders in the network depends on properties of the connectivity distribution.

Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Identification of optimal structural connectivity using functional connectivity and neural modeling.

The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.