Abstract. We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals.arXiv:1701.08427v2 [cond-mat.stat-mech]

Abstract. The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for simple models. We employ a numerical method based on rational interpolations to extrapolate the entanglement entropy of two disjoint intervals for the conformal field theories given by the free compact boson and the Ising model. The case of three disjoint intervals is studied for the Ising model and the non compact free massless boson. For the latter model, the logarithmic negativity of two disjoint intervals has been also considered. Some of our findings have been checked against existing numerical results obtained from the corresponding lattice models.arXiv:1501.04311v1 [cond-mat.stat-mech]

Abstract. We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading order for large domains, the logarithmic negativity and the logarithm of the ratio between the generic moment of the partial transpose and the moment of the reduced density matrix at the same order satisfy an area law in terms of the length of the curve shared by the adjacent regions. We give numerical evidences that the coefficient of the area law term in these quantities is related to the coefficient of the area law term in the Rényi entropies. Whenever the curve shared by the adjacent domains contains vertices, a subleading logarithmic term occurs in these quantities and the numerical values of the corner function for some pairs of angles are obtained. In the special case of vertices corresponding to explementary angles, we provide numerical evidence that the corner function of the logarithmic negativity is given by the corner function of the Rényi entropy of order 1/2. arXiv:1604.02609v2 [cond-mat.stat-mech]

In this paper, we report upon our recent work aimed at improving and adapting machine learning algorithms to automatically classify nanoscience images acquired by the Scanning Electron Microscope (SEM). This is done by coupling supervised and unsupervised learning approaches. We first investigate supervised learning on a ten-category data set of images and compare the performance of the different models in terms of training accuracy. Then, we reduce the dimensionality of the features through autoencoders to perform unsupervised learning on a subset of images in a selected range of scales (from 1 μm to 2 μm). Finally, we compare different clustering methods to uncover intrinsic structures in the images.