We analyze the behavior of the dynamic scattering amplitude between Fermi liquid quasiparticles at the Fermi surface in the proximity of a charge instability, which may occur in the high temperature superconducting cuprates. Within the infinite-U Hubbard-Holstein model in the slave-boson large-N technique we find that, in the absence of long-range Coulomb forces the scattering amplitude is strongly singular at zero momentum transfer close to the phase separation instability and it has the same form provided by gauge-field theories. In the presence of long-range Coulomb forces the charge instability occurs at finite wavevectors and concomitantly the scattering is still singular but anisotropic. Nevertheless it remains strong over extended regions of the momentum space. In both cases we show how normal state properties are largely affected by this scattering. 71.27.+a, It is generally accepted that the understanding of the pairing mechanism in high T c superconductors is related to the understanding of the anomalous behaviour of the normal phase.The anomalous properties of the normal phase have been interpreted along two distinct theoretical lines. One possible explanation is that the low dimensionality of these highly anisotropic systems and their correlated nature are at the origin of a breakdown of the Fermi liquid (FL).In particular the proposal of a Luttinger liquid formation in two dimension [1] has been intensively investigated [2]. The alternative aptitude has been to accept the Landau theory of normal FL's as a suitable starting point. The anomalous properties would then arise as a consequence of strong scattering processes at low energy between the quasiparticles. Along this line magnetic scattering has been considered to be responsible for both the anomalous properties of the normal phase and for the superconducting pairing [3]. Strong scattering may even lead to a complete disruption of the FL phase. In particular it was proposed that excitonic scattering could give rise to the so called marginal FL [4], and could also provide a pairing mechanism. Singular scattering can also be provided by gauge fields [5], which arise by implementing the resonating-valence-bond idea in the t-J model.In this letter we want to understand whether phase separation (PS) or the incommensurate charge density wave (ICDW) instability are sources of strong scattering besides the above mechanisms. Indeed the complex nature of the phase diagram as a function of doping and temperature indicates that various energy scales of different nature (magnetic, excitonic,...) of the same order of magnitude compete to determine the low-energy physics and may lead to various instabilities, among which PS or charge instabilities may play a relevant role.After PS was shown to be present in the phase diagram of the t-J model [6,7], we pointed out that PS commonly occurs in models with short range interaction [8][9][10][11][12][13][14][15], provided the strong local e-e repulsion inhibits the stabilizing role of the kinetic energy. We therefor...

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We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, i.e. scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different "universality classes", and discuss the behavior of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class.The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective low-energy theories. Particular attention is payed to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.

Charge density waves are a common occurrence in all families of high critical temperature superconducting cuprates. Although consistently observed in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering we carefully determined the temperature dependence of charge density modulations in (Y,Nd)Ba2Cu3O7-δ for three doping levels. We discovered short-range dynamical charge density fluctuations besides the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of few meV and pervade a large area of the phase diagram, so that they can play a key role in shaping the peculiar normal-state properties of cuprates.Main text: High-Tc superconductors (HTS) are doped Mott insulators, where the quasi-twodimensionality of the layered structure and the large electron-electron repulsion (responsible, e.g., for the robust short-range antiferromagnetic correlations) make them deviating from the Landau Fermi liquid paradigm. The doping-temperature (p-T) phase diagram encompasses, at low T, the antiferromagnetic and the superconducting orders and, at higher T, the pseudogap region, which marks, below the cross-over temperature T*, a reduction of the quasiparticle density of states in some sections of the Fermi surface. In the pseudogap state and up to optimal doping p0.17, short/medium range incommensurate charge density waves (CDW) emerge as an order weakly competing with superconductivity.CDW were proposed theoretically since the early times of the high temperature superconductivity age (1,2,3); experimental evidence by surface and bulk sensitive techniques came initially in selected materials (4,5,6,7), and later in all cuprate families (8,9,10,11,12). Moreover long-range tridimensional CDW (3D-CDW) order has been observed inside the superconductive dome (for p0.08-0.17) in special circumstances, e.g. in high magnetic fields that weaken superconductivity or in epitaxially grown samples (13,14,15). Finally, it has come as a surprise the recent observation of CDW modulations in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime too (16), hinting at a wider than expected occurrence of this phenomenon.

We investigate the density instabilities present in the infinite-U Hubbard-Holstein model both at zero and finite momenta as well as the occurrence of Cooper instabilities with a specific emphasis on the role of long-range Coulomb forces. In carrying out this analysis a special attention is devoted to the effects of the strong local e-e interaction on the e-ph coupling and particularly to both the static and dynamic screening processes dressing this coupling. We also clarify under which conditions in strongly correlated electron systems a weak additional interaction, e.g. a phonon-mediated attraction, can give rise to a charge instability. In the presence of long-range Coulomb forces, the frustrated phase separation leads to the formation of incommensurate charge density waves. These instabilities, in turn, lead to strong residual scattering processes between quasiparticles and to superconductivity, thus providing an interesting clue to the interpretation of the physics of the copper oxides.