We tutorially review the determinantal Quantum Monte Carlo method for fermionic systems, using the Hubbard model as a case study. Starting with the basic ingredients of Monte Carlo simulations for classical systems, we introduce aspects such as importance sampling, sources of errors, and finite-size scaling analyses. We then set up the preliminary steps to prepare for the simulations, showing that they are actually carried out by sampling discrete Hubbard-Stratonovich auxiliary fields. In this process the Green's function emerges as a fundamental tool, since it is used in the updating process, and, at the same time, it is directly related to the quantities probing magnetic, charge, metallic, and superconducting behaviours. We also discuss the as yet unresolved 'minus-sign problem', and two ways to stabilize the algorithm at low temperatures.

The critical temperature for the attractive Hubbard model on a square lattice is determined from the analysis of two independent quantities, the helicity modulus s and the pairing correlation function P s . These quantities have been calculated through quantum Monte Carlo simulations for lattices up to 18ϫ18, and for several densities, in the intermediate-coupling regime. Imposing the universal-jump condition for an accurately calculated s , together with thorough finite-size scaling analyses ͑in the spirit of the phenomenological renormalization group͒ of P s , suggests that T c is considerably higher than hitherto assumed.

We address the question of weak versus strong universality scenarios for the random-bond Ising model in two dimensions. A finite-size scaling theory is proposed, which explicitly incorporates ln L corrections (L is the linear finite size of the system) to the temperature derivative of the correlation length. The predictions are tested by considering long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings, along which free energy, spin-spin correlation functions and specific heats are calculated by transfer-matrix methods. The ratio γ/ν is calculated and has the same value as in the pure case; consequently conformal invariance predictions remain valid for this type of disorder. Semilogarithmic plots of correlation functions against distance yield average correlation lengths ξ av , whose size dependence agrees very well with the proposed theory. We also examine the size dependence of the specific heat, which clearly suggests a divergency in the thermodynamic limit. Thus our data consistently favour the Dotsenko-Shalaev picture of logarithmic corrections (enhancements) to pure system singularities, as opposed to the weak universality scenario.

Light propagation through 1D disordered structures composed of alternating layers, with random thicknesses, of air and a dispersive metamaterial is theoretically investigated. Both normal and oblique incidences are considered. By means of numerical simulations and an analytical theory, we have established that Anderson localization of light may be suppressed: (i) in the long wavelength limit, for a finite angle of incidence which depends on the parameters of the dispersive metamaterial; (ii) for isolated frequencies and for specific angles of incidence, corresponding to Brewster anomalies in both positive-and negative-refraction regimes of the dispersive metamaterial. These results suggest that Anderson localization of light could be explored to control and tune light propagation in disordered metamaterials.

We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, ξ ave , are computed) by transfer-matrix methods. An ansatz for the size-dependence of logarithmic corrections to ξ ave is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with ν = 1) is recovered if these corrections are incorporated, discarding the weak-universality scenario.

We investigate Luttinger liquid superlattices, periodic structures composed of two kinds of one-dimensional systems of interacting electrons. We calculate several properties of the low-energy sector: the effective charge and spin velocities, the compressibility, various correlation functions, the Landauer conductance, and the Drude weight. The low-energy properties are subsumed into effective parameters, much like homogeneous onedimensional systems. A generic result is the weighted average nature of these parameters, in proportion to the spatial extent of the underlying subunits, pointing to the possibility of ''engineered'' structures. As a specific realization, we consider a one-dimensional Hubbard superlattice, which consists of a periodic arrangement of two long Hubbard chains with different coupling constants and different hopping amplitudes. This system exhibits a rich phase diagram with several phases, both metallic and insulating. We have found that gapless insulating phases are present over a wide range of parameters.

We study the Metal-Insulator transition in one-dimensional Hubbard superlattices (SL's), modelled by a repeated pattern of repulsive (i.e., positive on-site coupling) and free sites. The evolution of the local moment and of the charge gap (calculated from Lanczos diagonalization of chains up to 18 sites), together with a strong coupling analysis, show that the electron density at which the system is insulating increases with the size of the free layer, relative to the repulsive one. In the insulating state, the mechanism of interaction between fermions separated by a free layer is the analog of superexchange, and the charge gap display universal features. mit.tex -PACS: 71.30.+h 71.27.+a,

We use transfer-matrix methods to calculate free energies and specific heats on long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings. By implementation of our code on a highly parallel computer, we have managed to generate high-quality data for strip widths up to L = 18 sites. An unequivocal trend towards a divergency of the specific heat in the thermodynamic limit can be discerned. Finite-size data appear to behave halfway between a single- ( ln L) and double- ( ln ln L) logarithmic dependence on strip width. This is in line with a crossover within the Dotsenko-Shalaev picture of logarithmic corrections to pure-system singularities.