14,712 research outputs found
Luttinger liquid, singular interaction and quantum criticality in cuprate materials
With particular reference to the role of the renormalization group approach
and Ward identities, we start by recalling some old features of the
one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior.
Its dimensional crossover to the Landau normal Fermi liquid implies that a
non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature
superconductors, can be maintained in d>1, only in the presence of a
sufficiently singular effective interaction among the charge carriers. This is
the case when, nearby an instability, the interaction is mediated by
fluctuations. We are then led to introduce the specific case of
superconductivity in cuprates as an example of avoided quantum criticality. We
will disentangle the fluctuations which act as mediators of singular
electron-electron interaction, enlightening the possible order competing with
superconductivity and a mechanism for the non-Fermi-liquid behavior of the
metallic phase. This paper is not meant to be a comprehensive review. Many
important contributions will not be considered. We will also avoid using
extensive technicalities and making full calculations for which we refer to the
original papers and to the many good available reviews. We will here only
follow one line of reasoning which guided our research activity in this field.Comment: 23 pages, 10 figure
Phase separation frustrated by the long range Coulomb interaction II: Applications
The theory of first order density-driven phase transitions with frustration
due to the long range Coulomb (LRC) interaction develop on paper I of this
series is applied to the following physical systems: i) the low density
electron gas ii) electronic phase separation in the low density three
dimensional model iii) in the manganites near the charge ordered phase.
We work in the approximation that the density within each phase is uniform and
we assume that the system separates in spherical drops of one phase hosted by
the other phase with the distance between drops and the drop radius much larger
than the interparticle distance. For i) we study a well known apparent
instability related to a negative compressibility at low densities. We show
that this does not lead to macroscopic drop formation as one could expect
naively and the system is stable from this point of view. For ii) we find that
the LRC interaction significantly modifies the phase diagram favoring uniform
phases and mixed states of antiferromagnetic (AF) regions surrounded by
metallic regions over AF regions surrounded by empty space. For iii) we show
that the dependence of local densities of the phases on the overall density
found in paper I gives a non-monotonous behavior of the Curie temperature on
doping in agreement with experiments.Comment: Second part of cond-mat/0010092 12 pages, 12 figure
Coarse grained models in Coulomb-frustrated phase separation
Competition between interactions on different length scales leads to
self-organized textures in classical as well as quantum systems. This pattern
formation phenomenon has been invoked to explain some intriguing properties of
a large variety of strongly correlated electronic systems that includes for
example high temperature superconductors and colossal magnetoresistance
manganites. We classify the more common situations in which Coulomb frustrated
phase separation can occur and review their properties.Comment: 13 pages, 4 figures. Presented at "Phase Separation in Electronic
Systems", Crete 200
Electron-phonon coupling close to a metal-insulator transition in one dimension
We consider a one-dimensional system of electrons interacting via a
short-range repulsion and coupled to phonons close to the metal-insulator
transition at half filling. We argue that the metal-insulator transition can be
described as a standard one dimensional incommensurate to commensurate
transition, even if the electronic system is coupled to the lattice distortion.
By making use of known results for this transition, we prove that low-momentum
phonons do not play any relevant role close to half-filling, unless their
coupling to the electrons is large in comparison with the other energy scales
present in the problem. In other words the effective strength of the
low-momentum transferred electron-phonon coupling does not increase close to
the metal-insulator transition, even though the effective velocity of the
mobile carriers is strongly diminished.Comment: 20 pages, REVTEX styl
Phase separation frustrated by the long range Coulomb interaction I: Theory
We analyze the combined effect of the long range Coulomb (LRC) interaction
and of surface energy on first order density-driven phase transitions in the
presence of a compensating rigid background. We study mixed states formed by
regions of one phase surrounded by the other in the case in which the scale of
the inhomogeneities is much larger than the interparticle distance. Two
geometries are studied in detail: spherical drops of one phase into the other
and a layered structure of one phase alternating with the other. We find the
optimum density profile in an approximation in which the free energy is a
functional of the local density (LDA). It is shown that an approximation in
which the density is assumed to be uniform (UDA) within each phase region gives
results very similar to those of the more involved LDA approach. Within the UDA
we derive the general equations for the chemical potential and the pressures of
each phase which generalize the Maxwell construction to this situation. The
equations are valid for a rather arbitrary geometry. We find that the
transition to the mixed state is quite abrupt i.e. inhomogeneities of the first
phase appear with a finite value of the radius and of the phase volume
fraction. The maximum size of the inhomogeneities is found to be on the scale
of a few electric field screening lengths. Contrary to the ordinary Maxwell
construction, the inverse specific volume of each phase depends here on the
global density in the coexistence region and can decrease as the global density
increases. The range of densities in which coexistence is observed shrinks as
the LRC interaction increases until it reduces to a singular point. We argue
that close to this singular point the system undergoes a lattice instability as
long as the inverse lattice compressibility is finite.Comment: 17 pages, 14 figures. We added a section were the density profile of
inhomogeneities is arbitrary and included other geometries. The applications
of the original version are in a separate pape
Renormalization group and Ward identities in quantum liquid phases and in unconventional critical phenomena
By reviewing the application of the renormalization group to different
theoretical problems, we emphasize the role played by the general symmetry
properties in identifying the relevant running variables describing the
behavior of a given physical system. In particular, we show how the constraints
due to the Ward identities, which implement the conservation laws associated
with the various symmetries, help to minimize the number of independent running
variables. This use of the Ward identities is examined both in the case of a
stable phase and of a critical phenomenon. In the first case we consider the
problems of interacting fermions and bosons. In one dimension general and
specific Ward identities are sufficient to show the non-Fermi-liquid character
of the interacting fermion system, and also allow to describe the crossover to
a Fermi liquid above one dimension. This crossover is examined both in the
absence and presence of singular interaction. On the other hand, in the case of
interacting bosons in the superfluid phase, the implementation of the Ward
identities provides the asymptotically exact description of the acoustic
low-energy excitation spectrum, and clarifies the subtle mechanism of how this
is realized below and above three dimensions. As a critical phenomenon, we
discuss the disorder-driven metal-insulator transition in a disordered
interacting Fermi system. In this case, through the use of Ward identities, one
is able to associate all the disorder effects to renormalizations of the Landau
parameters. As a consequence, the occurrence of a metal-insulator transition is
described as a critical breakdown of a Fermi liquid.Comment: 47 pages, 11 figure
Gap and pseudogap evolution within the charge-ordering scenario for superconducting cuprates
We describe the spectral properties of underdoped cuprates as resulting from
a momentum-dependent pseudogap in the normal state spectrum. Such a model
accounts, within a BCS approach, for the doping dependence of the critical
temperature and for the two-parameter leading-edge shift observed in the
cuprates. By introducing a phenomenological temperature dependence of the
pseudogap, which finds a natural interpretation within the stripe
quantum-critical-point scenario for high-T_c superconductors, we reproduce also
the T_c-T^* bifurcation near optimum doping. Finally, we briefly discuss the
different role of the gap and the pseudogap in determining the spectral and
thermodynamical properties of the model at low temperatures.Comment: 13 pages (EPY style), 7 enclosed figures, to appear on Eur. Phys. J.
Collective transport and optical absorption near the stripe criticality
Within the stripe quantum critical point scenario for high
superconductors, we point out the possible direct contribution of charge
collective fluctuations to the optical absorption and to the d.c. resistivity.Comment: 2 pages 2 figures 1 style fil
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