Related papers: Crystallography of Hyperbolic Lattices
The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior…
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals. In this paper we study the embedding properties of spaces…
In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high…
Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting many-body systems. Their essential merit lies…
Moire lattices consist of two identical periodic structures overlaid with a relative rotation angle. Present even in everyday life, moire lattices have been also produced, e.g., with coupled graphene-hexagonal boron nitride monolayers,…
We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of…
Topological photonics has attracted widespread research attention in the past decade due to its fundamental interest and unique manner in controlling light propagation for advanced applications. Paradigmatic approaches have been proposed to…
Developing a non-compact version of the SUSY Hopf map, we formulate the quantum Hall effect on a super-hyperboloid. Based on $OSp(1|2)$ group theoretical methods, we first analyze the one-particle Landau problem, and successively explore…
This Part establishes the geometric theory of uniformly hyperbolic sets with explicit quantitative bounds throughout, and contains five main theorems. The Stable Manifold Theorem is proved via the backward graph transform, with a complete…
Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…
We investigate the holographic fermions over a gravitational lattice background with a rather low temperature. Since the rotation symmetry is broken on the plane, the lattice effects change the shape of the Fermi surface within the first…
The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…
Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological…
Let M_0^R be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H^4…
We develop a comprehensive theory for the effective dynamics of Bloch electrons based on symmetry. We begin with a scheme to systematically derive the irreducible representations (IRs) characterizing the Bloch functions. Starting from a…
Crystalline symmetry can be used to predict bulk and surface properties of topological phases. For non-interacting cases, symmetry-eigenvalue analysis of Bloch states at high symmetry points in the Brillouin zone simplifies the calculation…
Many geometric structures associated to surface groups can be encoded in terms of invariant cross ratios on their circle at infinity; examples include points of Teichm\"uller space, Hitchin representations and geodesic currents. We add to…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
In this thesis, I am going to consider Bernoulli percolation on graphs admitting vertex-transitive actions of groups of isometries of d-dimensional hyperbolic spaces H^d. In the first chapter, I give an overview concerning percolation and…
Recent advances in twistronics of low-dimensional materials, such as bilayer graphene and transition-metal dichalcogenides, have enabled a plethora of unusual phenomena associated with moir\'e physics. However, several of these effects…