We show that introducing long-range Coulomb interactions immediately lifts the massive ground state degeneracy induced by geometric frustration for electrons on quarter-filled triangular lattices in the classical limit. Important consequences include the stabilization of a stripe-ordered crystalline (global) ground state, but also the emergence of very many low-lying metastable states with amorphous "stripe-glass" spatial structures. Melting of the stripe order thus leads to a frustrated Coulomb liquid at intermediate temperatures, showing remarkably slow (viscous) dynamics, with very long relaxation times growing in Arrhenius fashion upon cooling, as typical of strong glass formers. On shorter time scales, the system falls out of equilibrium and displays the aging phenomena characteristic of supercooled liquids above the glass transition. Our results show remarkable similarity with the recent observations of charge-glass behavior in ultra-clean triangular organic materials of the θ-(BEDT-TTF)2 family. Metastability, slow relaxation, and other features of glassy dynamics are often observed in electronic systems at the brink of the metal-insulator transition [1]. These effects, however, are typically attributed to disorder caused by impurities or defects, rather than being an intrinsic feature of strongly interacting electrons. Indeed, "Coulomb glass" behavior [2, 3] is well established in disordered insulators [4,5]; in other cases metastability can be caused by disorder-dominated phase separation in presence of competing orders [6].A more intriguing possibility was proposed in the heyday of cuprate superconductivity, with the idea of "Coulomb-frustrated phase separation" in lightly doped Mott insulators [7,8]. It suggested the possibility of spontaneous (disorder-unrelated) formation of many complicated patterns of charge density, such as bubbles and stripe crystals [9], or even stripe glasses [10]. Unfortunately, no conclusive theoretical or experimental evidence emerged to support the existence of such phase separation, which long remained more of a theorist's dream than an accepted mechanism for metastability in electronic systems.Glassy freezing without disorder, on the other hand, is well established in several systems with geometric frustration, most notably the supercooled liquids [11]. A natural question thus emerges: can sufficient geometric frustration cause disorder-free glassy behavior of electrons, in (many) situations where phase separation effects are not relevant? Geometric frustration arises, for example, in spin systems on triangular lattices [12,13], sometimes leading to exotic phases like spin liquids [14]; related frustration-driven phenomena in the charge sector have been little explored so far.A class of systems where one can directly investigate these important questions is represented by the organic triangular compounds of the family θ-(BEDT-TTF) 2 M M (SCN) 4 (in short θ-M M ) where M =Tl,Rb, Cs and M = Co,Zn, which exhibits a notable degree of charge frustration [15]. These materials ...

We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum-resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one-dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power law, Wc ∼ (1/Lc)(1/ν), whereas in two-dimensions, the critical disorder strength decreases logarithmically with the linear cluster size. Our results are consistent with previous numerical work and are in agreement with the one-parameter scaling theory.

The one-dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising-type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction ͑J͒ between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value J c . Moreover, our results show that the onset of anisotropy in the XY term of the itinerant interactions develops the antiferromagnetic order for J Ͻ J c . This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic XY interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.

We present a complete analytical and numerical solution of the Typical Medium Theory (TMT) for the Anderson metal-insulator transition. This approach self-consistently calculates the typical amplitude of the electronic wave-functions, thus representing the conceptually simplest order-parameter theory for the Anderson transition. We identify all possible universality classes for the critical behavior, which can be found within such a meanfield approach. This provides insights into how interaction-induced renormalizations of the disorder potential may produce qualitative modifications of the critical behavior. We also formulate a simplified description of the leading critical behavior, thus obtaining an effective Landau theory for Anderson localization.