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Using the Matrix Product State framework, we generalize the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids with global color SU(N) symmetry, finite correlation lengths, and edge states that can belong to any self-conjugate ...
The conformal bootstrap is a non-perturbative technique designed to study conformal field theories using only first principles, such as unitarity, crossing symmetry and the existence of an Operator Product Expansion. In this thesis we discuss an applicatio ...
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...
We study the angular scattering behavior of bianisotropic metasurfaces and deduce relationships between the corresponding symmetrical angular scattering properties and the structural symmetries of their scattering particles. This may be of practical intere ...
Guiding electromagnetic energy at a subwavelength scale is one of the most highly demanded functionalities in a variety of applications, including compact, lightweight satellite communications, signal and data processing, and power systems. The existing sc ...
Convolutional neural networks (CNNs) are powerful tools in Deep Learning mainly due to their ability to exploit the translational symmetry present in images, as they are equivariant to translations. Other datasets present different types of symmetries (e.g ...
In this paper, we verify the large scale structure consistency relations using N-body simulations, including modes in the highly nonlinear regime. These relations (pointed out by Kehagias & Riotto and Peloso & Pietroni) follow from the symmetry of the dyna ...
Cellular checkerboard patterns are observed at many stages of embryonic development. We study an analytically tractable model for lateral inhibition and show that the steady states are analogous to optical phonons at the Gamma point, which have the wave nu ...
We study the zero-temperature phase diagram of the spin-1/2 Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simul ...
Transport properties of particles in confining geometries show very specific characteristics as lateral drift, oscillatory movement between lateral walls or the deformation of flexible fibers. These dynamics result from viscous friction with transversal an ...