The Metal-Insulator Transition in the Hubbard Model at Zero Temperature II

We study the metal-to-insulator transition of the Hubbard model at zero temperatures in infinite dimensions. The coexistence of metallic and insulating solutions for a finite range of the interaction is established. It is shown that the metallic solution is lower in energy for any interaction in the coexistence region and that the transition is of second order.Comment: 12 pages, revte

Dynamical Mean Field Theory with the Density Matrix Renormalization Group

A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.Comment: 5 pages, 4 figure

Quantum Monte Carlo method for models of molecular nanodevices

We introduce a quantum Monte Carlo technique to calculate exactly at finite temperatures the Green function of a fermionic quantum impurity coupled to a bosonic field. While the algorithm is general, we focus on the single impurity Anderson model coupled to a Holstein phonon as a schematic model for a molecular transistor. We compute the density of states at the impurity in a large range of parameters, to demonstrate the accuracy and efficiency of the method. We also obtain the conductance of the impurity model and analyze different regimes. The results show that even in the case when the effective attractive phonon interaction is larger than the Coulomb repulsion, a Kondo-like conductance behavior might be observed.Comment: 5 pages, 4 figure

Solid State Neuroscience: Spiking Neural Networks as Time Matter

We aim at building a bridge between to {\it a priori} disconnected fields: Neuroscience and Material Science. We construct an analogy based on identifying spikes events in time with the positions of particles of matter. We show that one may think of the dynamical states of spiking neurons and spiking neural networks as {\it time-matter}. Namely, a structure of spike-events in time having analogue properties to that of ordinary matter. We can define for neural systems notions equivalent to the equations of state, phase diagrams and their phase transitions. For instance, the familiar Ideal Gas Law relation (P$v$ = constant) emerges as analogue of the Ideal Integrate and Fire neuron model relation ($I_{in}$ISI = constant). We define the neural analogue of the spatial structure correlation function, that can characterize spiking states with temporal long-range order, such as regular tonic spiking. We also define the ``neuro-compressibility'' response function in analogy to the lattice compressibility. We show that similarly to the case of ordinary matter, the anomalous behavior of the neuro-compressibility is a precursor effect that signals the onset of changes in spiking states. We propose that the notion of neuro-compressibility may open the way to develop novel medical tools for the early diagnose of diseases. It may allow to predict impending anomalous neural states, such as Parkinson's tremors, epileptic seizures, electric cardiopathies, and perhaps may even serve as a predictor of the likelihood of regaining consciousness.Comment: 8 pages, 8 figure