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

Generating Diophantine Sets by Virus Machines

Virus Machines are a computational paradigm inspired by the manner in which viruses replicate and transmit from one host cell to another. This paradigm provides non-deterministic sequential devices. Non-restricted virus machines are unbounded virus machines, in the sense that no restriction on the number of hosts, the number of instructions and the number of viruses contained in any host along any computation is placed on them. The computational completeness of these machines has been obtained by simulating register machines. In this paper, virus machines as set generating devices are considered. Then, the universality of non-restricted virus machines is proved by showing that they can compute all diophantine sets, which the MRDP theorem proves that coincide with the recursively enumerable sets.Ministerio de Economía y Competitividad TIN2012- 3743

The Mott transition in V_2 O_3 and Ni Se_x S_{2-x}: insights from dynamical mean field theory

We discuss some aspects of the pressure (or interaction) driven Mott transition, in three dimensional transition metal oxides by means of dynami cal mean field theory. We isolate the universal properties of the transition from the aspects which depend more on the detailed chemistry of the compounds. In this light we can understand the main differences and the remarkable similarities between these systems. Both theory and experiment converge on the transfer of spectral weight from low energies to high energies as the universal mechanism underlying the Mott transition, and we comment on the possible relevance of these ideas to other metal to non metal transitions.Comment: Talk presented at SCES 9

Equational reasoning with context-free families of string diagrams

String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of context-free grammars, called B-ESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21145-9_

Metal-Insulator transitions in the periodic Anderson model

We solve the Periodic Anderson model in the Mott-Hubbard regime, using Dynamical Mean Field Theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the Periodic Anderson model, even in the Mott-Hubbard regime.Comment: 5 pages, 4 figure