M. Ortuño

Explicit Local Integrals of Motion for the Many-Body Localized State.

Recently, it has been suggested that the many-body localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert-space-preserving renormalization scheme that iteratively finds such integrals of motion exactly. Our method is based on the consecutive action of a similarity transformation using displacement operators. We show, as a proof of principle, localization and the delocalization transition in interacting fermion chains with random on-site potentials. Our scheme of consecutive displacement transformations can be used to study many-body localization in any dimension, as well as disorder-free Hamiltonians.

Percolation and motion in a simple random environment

The authors present a particularly simple model of deterministic classical motion in a two-dimensional random environment. As the parameters of the model are varied, a transition occurs from all trajectories being localised to some being extended. They construct a mean-field theory for this transition, and relate the model exactly to percolation models in particular parameter ranges. They point out that it is a member of a new class of site percolation analogues of direct bond percolation.

Fluctuations of the correlation dimension at metal-insulator transitions

We investigate numerically the inverse participation ratio, P(2), of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of lnP(2) scales with system size L as sigma(2)(L) = sigma(2)(infinity)-AL(-D(2)/2d), with D(2) being the correlation dimension and d the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for b = 0.3 (see the text for the definition of b) are fairly similar with respect to all critical magnitudes studied.

3D loop models and the CP(n-1) sigma model.

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to CP(n-1) sigma models, where n is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for n=1, 2, 3, and first order transitions for n≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.

Anomalously large critical regions in power-law random matrix ensembles

We investigate numerically the power-law random matrix ensembles. Wave functions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size. The Greens functions decrease with distance as a power law with an exponent related to the correlation dimension.

Negative magnetoresistance in ultrananocrystalline diamond: Strong or weak localization?

Electronic transport of ultrananocrystalline diamond involves the interplay between disorder, Anderson localization, and phase coherence. We show that variable range hopping explains many key features of the conductivity including the large low temperature negative magnetoresistance. Our numerical studies suggest two regimes where the (negative) magnetoresistance varies with magnetic field B such as B2 or B1∕2, respectively, depending on the ratio of the cyclotron orbital radius and the hopping distance. This agrees with experiment, which also points to the expected T−1∕2 temperature dependence of the hopping distance at the critical field.

Length distributions in loop soups.

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using CP(n-1) or RP(n-1) and O(n) σ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter θ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.

Localized to extended states transition for two interacting particles in a two-dimensional random potential

We show by a numerical procedure that a short-range interaction u induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dysons equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by a scaling analysis of the renormalized decay length of the bars. For u = 1, the critical disorder found is Wc = 9.3 ± 0.2, and the critical exponent ν = 2.4 ± 0.5. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected.

Many-particle jumps algorithm and Thomson's problem

We study Thomsons problem using a new numerical algorithm, valid for any interacting complex system based on the consideration of simultaneous many-particle transitions to reduce the characteristic slowing down of numerical algorithms when applied to critical or complex systems. We improve or reproduce all previous results on the Thomson problem, using much less computer time than the other numerical algorithms. We report ground-state energies for , and study the stability of the ground state as a function of the number of charges considered. We associate this stability with how well defined are the charges surrounded by five nearest neighbours, whose number always seems to be equal to 12.

Phase transitions in three-dimensional loop models and the C P n − 1 sigma model

We consider the statistical mechanics of a class of models involving close-packed loops with fugacity