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 ϵ\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

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

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

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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