相关论文: Classification of point-group-symmetric orientatio…
Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly non-trivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal…
The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries $O(3)$ of isotropic space to a discrete subgroup, i.e. a three-dimensional point group. The subgroups form a rich hierarchy and allow for…
A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot…
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding…
The symmetry-constrained response tensors on transport, optical, and electromagnetic effects are of central importance in condensed matter physics because they can guide experimental detections and verify theoretical calculations. These…
In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by…
We consider an infinitesimal volume where there are many rigid molecules of the same kind, and discuss the description and classification of the local anisotropy in this volume by tensors. First, we examine the symmetry of a rigid molecule,…
The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor $\mathbb{S}$. When this is calculated through experiments or simulations, the symmetry group of the phase is not known…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…
A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries.…
Spontaneous symmetry breaking is well understood through the classical "Mexican Hat" picture, which describes many quantum phases of matter. Recently, several new classes of quantum phases of matter, such as topological orders and symmetry…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Octupolar tensors are third order, completely symmetric and traceless tensors. Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle and can ultimately be identified with a vector in the plane, the symmetries…
Magnetism has witnessed remarkable progress in recent decades, largely driven by its potential for next-generation storage devices. However, the classification of magnetic orders, even for fundamental concepts such as ferromagnetism and…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…
For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in…