168 research outputs found

### Dielectric function and plasmons of doped three-dimensional Luttinger semimetals

Luttinger semimetals are three-dimensional electron systems with a parabolic
band touching and an effective total spin $J=3/2$. In this paper, we present an
analytical theory of dielectric screening of inversion-symmetric Luttinger
semimetals with an arbitrary carrier density and conduction-valence effective
mass asymmetry. Assuming a spherical approximation for the single-particle
Luttinger Hamiltonian, we determine analytically the dielectric screening
function in the random phase approximation for arbitrary values of the wave
vector and frequency, the latter in the complex plane. We use this analytical
expression to calculate the dispersion relation and Landau damping of the
collective modes in the charge sector (i.e., plasmons).Comment: 17 pages, 5 figures, published versio

### Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach

We study the scaling behavior of two-dimensional (2D) crystalline membranes
in the flat phase by a renormalization group (RG) method and an
$\epsilon$-expansion. Generalization of the problem to non-integer dimensions,
necessary to control the $\epsilon$-expansion, is achieved by dimensional
continuation of a well-known effective theory describing out-of-plane
fluctuations coupled to phonon-mediated interactions via a scalar composite
field, equivalent for small deformations to the local Gaussian curvature. The
effective theory, which will be referred to as Gaussian curvature interaction
(GCI) model, is equivalent to theories of elastic $D$-dimensional manifolds
fluctuating in a $(D + d_{c})$-dimensional embedding space in the physical case
$D = 2$ for arbitrary $d_{c}$. For $D\neq 2$, instead, the GCI model is not
equivalent to a direct dimensional continuation of elastic membrane theory and
it defines an alternative generalization to generic internal dimension $D$. We
calculate explicitly RG functions at two-loop order and determine the exponent
$\eta$ characterizing the long-wavelength scaling of correlation functions to
order $\epsilon^{2}$ in an $\epsilon=(4-D)$-expansion. The self-consistent
screening approximation (SCSA) for the GCI model is shown to be exact to
O($\epsilon^{2}$). For $d_{c} = 1$, the O($\epsilon^{2}$) correction is
suppressed by a small numerical prefactor. As a result, despite the large value
of $\epsilon = 2$, extrapolation of the first and second order results to $D =
2$ leads to very close numbers, $\eta = 0.8$ and $\eta \simeq 0.795$. The
calculated exponent values are close to earlier reference results obtained by
non-perturbative RG, the SCSA and numerical simulations. These indications
suggest that a perturbative analysis of the GCI model could provide an useful
framework for accurate quantitative predictions of the scaling exponent even at
$D = 2$.Comment: 15 pages, 4 figure

### Frustrated magnets in the limit of infinite dimensions: dynamics and disorder-free glass transition

We study the statistical mechanics and the equilibrium dynamics of a system
of classical Heisenberg spins with frustrated interactions on a $d$-dimensional
simple hypercubic lattice, in the limit of infinite dimensionality $d \to
\infty$. In the analysis we consider a class of models in which the matrix of
exchange constants is a linear combination of powers of the adjacency matrix.
This choice leads to a special property: the Fourier transform of the exchange
coupling $J(\mathbf{k})$ presents a $(d-1)$-dimensional surface of degenerate
maxima in momentum space. Using the cavity method, we find that the statistical
mechanics of the system presents for $d \to \infty$ a paramagnetic solution
which remains locally stable at all temperatures down to $T = 0$. To
investigate whether the system undergoes a glass transition we study its
dynamical properties assuming a purely dissipative Langevin equation, and
mapping the system to an effective single-spin problem subject to a colored
Gaussian noise. The conditions under which a glass transition occurs are
discussed including the possibility of a local anisotropy and a simple type of
anisotropic exchange. The general results are applied explicitly to a simple
model, equivalent to the isotropic Heisenberg antiferromagnet on the
$d$-dimensional fcc lattice with first and second nearest-neighbour
interactions tuned to the point $J_{1} = 2J_{2}$. In this model, we find a
dynamical glass transition at a temperature $T_{\rm g}$ separating a
high-temperature liquid phase and a low temperature vitrified phase. At the
dynamical transition, the Edwards-Anderson order parameter presents a jump
demonstrating a first-order phase transition.Comment: 24 page

### Scale without conformal invariance in membrane theory

We investigate the relation between dilatation and conformal symmetries in
the statistical mechanics of flexible crystalline membranes. We analyze, in
particular, a well-known model which describes the fluctuations of a continuum
elastic medium embedded in a higher-dimensional space. In this theory, the
renormalization group flow connects a non-interacting ultraviolet fixed point,
where the theory is controlled by linear elasticity, to an interacting infrared
fixed point. By studying the structure of correlation functions and of the
energy-momentum tensor, we show that, in the infrared, the theory is only
scale-invariant: the dilatation symmetry is not enhanced to full conformal
invariance. The model is shown to present a non-vanishing virial current which,
despite being non-conserved, maintains a scaling dimension exactly equal to $D
- 1$, even in presence of interactions. We attribute the absence of anomalous
dimensions to the symmetries of the model under translations and rotations in
the embedding space, which are realized as shifts of phonon fields, and which
protect the renormalization of several non-invariant operators. We also note
that closure of a symmetry algebra with both shift symmetries and conformal
invariance would require, in the hypothesis that phonons transform as primary
fields, the presence of new shift symmetries which are not expected to hold on
physical grounds. We then consider an alternative model, involving only scalar
fields, which describes effective phonon-mediated interactions between local
Gaussian curvatures. The model is described in the ultraviolet by two copies of
the biharmonic theory, which is conformal, but flows in the infrared to a fixed
point which we argue to be only dilatation-invariant.Comment: 30 page

### Napoli. Galleria Principe di Napoli

Siglo XIX. Forma parte del álbum 17 Souvenir de Naples. Álbu

### Napoli. Piazza del Carmine

Siglo XIX. Forma parte del álbum 17 Souvenir de Naples. Álbu

### Napoli. Stazione della Ferropia

Siglo XIX. Forma parte del álbum 17 Souvenir de Naples. Álbu

### Napoli. Villa Nazionale Riviera di Chiaia

Siglo XIX. Forma parte del álbum 17 Souvenir de Naples. Álbu

### Napoli. Santa Lucia

Siglo XIX. Forma parte del álbum 17 Souvenir de Naples. Álbu

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