arXiv subjects

C. Gros

Publications and source records attributed to C. Gros.

At least 19 recordsLinked to original sources

arXiv2012

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.

nlin.AO↗

arXiv2009

Semantic learning in autonomously active recurrent neural networks

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli. There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up? We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, {\it viz} the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

q-bio.NC↗

arXiv2009

Proximity of LaOFeAs to a magnetic instability

We investigate the effect of external pressure on the Fe magnetic moment in undoped LaOFeAs within the framework of density functional theory and show that this system is close to a magnetic instability: The Fe moment is found to drop by nearly a factor of 3 within a pressure range of $\pm$ 5 GPa around the calculated equilibrium volume. While the Fe moments show an unusually strong sensitivity to the spin arrangement (type of anti-ferromagnetic structure), the low temperature structural distortion is found to have only a minor influence on them. Analysis of the Fermi surface topology and nesting features shows that these properties change very little up to pressures of at least 10 GPa. We discuss the magnetic instability in terms of the itinerancy of this system.

cond-mat.supr-con↗

arXiv2007

Gutzwiller-RVB Theory of High Temperature Superconductivity: Results from Renormalised Mean Field Theory and Variational Monte Carlo Calculations

We review the Resonating Valence Bond (RVB) theory of high temperatur e superconductivity using Gutzwiller projected wave functions that incorporate strong correlations. After a general overview of the phenomenon of high temperature superconductivity, we discuss Anderson's RVB picture and its implementation by renormalised mean field theory (RMFT) and variational Monte Carlo (VMC) techniques. We review RMFT and VMC results with an emphasis on recent development s in extending VMC and RMFT techniques to excited states. We compare results obtained from these methods with angle resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM). We conclude by summarising recent successes of this approach and discuss open problems that need to be solved for a consistent and complete description of high temperature superconductivity using Gutzwiller projected wave functions.

cond-mat.str-el↗

arXiv2005

Ordering in Two-Dimensional Ising Models with Competing Interactions

We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular region of interactions, corresponding to the Ising sector's super-antiferromagnetic (SAF) ground state. The spin-SAF transition in the coupled Ising-XY model into a phase with co-existent SAF Ising (pseudospin) long-range order and a spin gap is considered. Along with destruction of the quantum critical point of the Ising sector, the phase digram of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase. A detailed study of the latter is presented. The mechanism of the re-entrance, due to interplay of interactions in the coupled model, and the conditions of its appearance are established. Applications of the spin-SAF theory for the transition in the quarter-filled ladder compound NaV2O5 are discussed.

cond-mat.stat-mech↗

arXiv2005

Na2V3O7, a frustrated nanotubular system with spin-1/2 diamond rings

Following the recent discussion on the puzzling nature of the interactions in the nanotubular system Na2V3O7, we present a detailed ab-initio microscopic analysis of its electronic and magnetic properties. By means of a non-trivial downfolding study we propose an effective model in terms of tubes of nine-site rings with the geometry of a spin-diamond necklace with frustrated inter-ring interactions. We show that this model provides a quantitative account of the observed magnetic behavior.

cond-mat.mtrl-sci↗

arXiv2005

On the evaluation of matrix elements in partially projected wave functions

We generalize the Gutzwiller approximation scheme to the calculation of nontrivial matrix elements between the ground state and excited states. In our scheme, the normalization of the Gutzwiller wave function relative to a partially projected wave function with a single non projected site (the reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we evaluate the relative normalization both analytically and by variational Monte-Carlo (VMC). We also report VMC results for projected superconducting states that show novel oscillations in the hole density near the reservoir site.

cond-mat.str-el↗

arXiv2005

Quantum Monte Carlo simulation for the spin-drag conductance of the Hubbard model

In the situation of two electro-statically coupled conductors a current in one conductor may induce a current in the other one. We will study this phenomenon, called Coulomb drag, in the Hubbard chain where the two ``conductors'' are given by fermions with different spin orientation. With the aid of a Monte Carlo (MC) approach which we presented in a recent paper we calculate the Transconductance in different variants of the Hubbard chain (with/without impurity and additional [long-ranged] interactions) for different fillings.

cond-mat.str-el↗

arXiv2004

On the Stacking Charge Order in NaV2O5

We propose a mechanism for the observed stacking charge order in the quarter-filled ladder compound NaV2O5. Via a standard mapping of the charge degrees of freedom onto Ising spins we explain the stacking order as a result of competition between couplings of the nearest and next-nearest planes with the 4-fold degenerate super-antiferroelectric in-plane order.

cond-mat.str-el↗

arXiv2003

A renormalised hamiltonian approach for a resonant valence bond wavefunction

The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalise the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using a Gutzwiller approximation scheme. The accuracy of this renormalisation procedure is tested numerically and found to be qualitatively excellent. Within the scheme a resonant valence bond (RVB) wavefunction is found at half-filling to be lower in energy than the antiferromagnetic state. If the wavefunction is expressed in fermion operators, local SU(2) and U(l) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and we find that a d-wave RVB state is lowest in energy. This state has a superconducting order parameter whose amplitude is linear in the density of holes.

cond-mat.str-el↗

arXiv2003

Simultaneous Charge Ordering and Spin Dimerization in Quasi-Two-Dimensional Quarter-Filled Ladders

We study the spin-pseudospin Hamiltonian of the Ising Model in Transverse Field (IMTF) for pseudospins, coupled to the XY-spins on a triangular lattice. This model appears from analyses of the quarter-filled ladder compound $NaV_2O_5$, and pseudospins represent its charge degrees of freedom. In the molecular-field approximation we find that the model possesses two phases: charge-disordered without spin gap; and a low-temperature phase containing both the anti-ferroelectric (zigzag) charge order and spin dimerization (spin gap). The phase transition is of the second kind, and the calculated physical quantities are as those one expects from the Landau theory. One of particular features of the phase diagram is that the inter-ladder spin-pseudospin coupling, responsible for the spin gap generation, also destroys the IMTF quantum critical point, resulting in the exponential behavior of $T_c$ in the region of Ising's coupling where the IMTF is always disordered. We conclude that our mean-field results give a qualitatively correct description of the phase transition in $NaV_2O_5$, while a more sophisticated analysis is warranted in order to take into account the thermal fluctuations and, probably, the proximity of the IMTF quantum critical point.

cond-mat.str-el↗

arXiv2003

Stochastic Cluster Series expansion for quantum spin systems

In this paper we develop a cluster-variant of the Stochastic Series expansion method (SCSE). For certain systems with longer-range interactions the SCSE is considerably more efficient than the standard implementation of the Stochastic Series Expansion (SSE), at low temperatures. As an application of this method we calculated the T=0-conductance for a linear chain with a (diagonal) next nearest neighbor interaction.

cond-mat↗

arXiv2003

Minimal charge gap in the ionic Hubbard model

We study the ionic Hubbard model at temperature T=0 within the mean-field approximation, and show that the charge gap does not close completely at the ionic-band insulator to antiferromagnetic insulator transition, contrary to previous expectations. Furthermore, we find an intermediate phase for on-site repulsions $U>U_c$ for different lattices, and calculate the phase diagram for the ionic Hubbard model with alternating U, corresponding to a Cu-O lattice.

cond-mat.str-el↗

arXiv2003

Magnetic Raman scattering of the ordered tetrahedral spin-1/2 clusters in Cu_2Te_2O_5(Br_(1-x)Cl_x)_2 compounds

Raman light-scattering experiments in the antiferromagnetic phase of the Cu_2Te_2O_5(Br_(1-x)Cl_x)_2 compounds are analyzed in terms of a dimerized spin model for the tetrahedral Cu-clusters. It is shown that the longitudinal magnetic excitation in the pure Br system hybridizes with a localized singlet excitation due to the presence of a Dzyaloshinskii-Moriya anisotropy term. The drastic change of the magnetic scattering intensities observed when a proportion of Br is replaced by Cl ions, is proposed to be caused by a change of the magnetic order parameter. Instead of being parallel/antiparallel with each other, the spins in the two pairs of spin-1/2 order perpendicular to each other, when the composition x is larger than about 0.25.

cond-mat.str-el↗

arXiv2003

Diverging magnetothermal response in the one-dimensional Heisenberg chain

A current of magnetic moments will flow in the spin-1/2 Heisenberg chain in the presence of an external magnetic field $B$ and a temperature gradient $ΔT$ along the chain. We show that this magnetothermal effect is strictly {\em infinite} for the integrable Heisenberg-model in one dimension. We set-up the response formalism and derive several new generalized Einstein relations for this magnetothermal effect which vanishes in the absence of an external magnetic field. We estimate the size of the magnetothermal response by exact diagonalization and Quantum Monte Carlo and make contact with recent transport measurements for the one-dimensional Heisenberg compound $\rm Sr_2CuO_3$.

cond-mat↗

arXiv2003

Longitudinal magnon in the tetrahedral spin system Cu2Te2O5Br2 near quantum criticality

We present a comprehensive study of the coupled tetrahedra-compound Cu2Te2O5Br2 by theory and experiments in external magnetic fields. We report the observation of a longitudinal magnon in Raman scattering in the ordered state close to quantum criticality. We show that the excited tetrahedral-singlet sets the energy scale for the magnetic ordering temperature T_N. This energy is determined experimentally. The ordering temperature T_N has an inverse-log dependence on the coupling parameters near quantum criticality.

cond-mat.str-el↗

arXiv2003

Magnetic light scattering in low-dimensional quantum spin systems

An overview of one- and two-dimensional quantum spin systems based on transition-metal oxides and halides of current interest is given, such as spin-Peierls, spin-dimer, geometrically frustrated and ladder systems. The most significant and outstanding contributions of magnetic light scattering to the understanding of these materials are discussed and compared to results of other spectroscopies and thermodynamic measurements.

cond-mat.str-el↗

arXiv2002

Quantum phase transition in the dioptase magnetic lattice

The study of quantum phase transitions, which are zero-temperature phase transitions between distinct states of matter, is of current interest in research since it allows for a description of low-temperature properties based on universal relations. Here we show that the crystal green dioptase Cu_6Si_6O_18 . 6H_2O, known to the ancient Roman as the gem of Venus, has a magnetic crystal structure, formed by the Cu(II) ions, which allows for a quantum phase transition between an antiferromagnetically ordered state and a quantum spin liquid.

cond-mat.str-el↗