Related papers: Projectively enriched symmetry and topology in aco…
Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After…
Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and…
For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological…
A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain…
Recently, novel crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitudes. We show that Cayley-Schreier lattices can…
While two-dimensional symmetry-enriched topological phases ($\mathsf{SET}$s) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
Non-Hermiticity significantly enriches the concepts of symmetry and topology in physics. Particularly, non-Hermiticity gives rise to the ramified symmetries, where the non-Hermitian Hamiltonian $H$ is transformed to $H^\dagger$. For…
We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with…
Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel topological phases. We show that the…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
Symmetry plays a key role in classifying topological phases. Recent theory shows that in the presence of gauge fields, the algebraic structure of crystalline symmetries needs to be projectively represented, which enables unprecedented…
Tunable symmetry breaking plays a crucial role for the manipulation of topological phases of quantum matter. Here, through combined high-pressure magneto-transport measurements, Raman spectroscopy, and X-ray diffraction, we demonstrate a…
Spatial symmetries appearing in both real and momentum space are of fundamental significance to crystals. However, in the conventional framework, every space group in real space, either symmorphic or nonsymmorphic, corresponds to a…
Structural symmetry of crystals plays important roles in physical properties of two-dimensional (2D) materials, particularly in the nonlinear optics regime. It has been a long-term exploration on the physical properties in 2D materials with…
In topological phases in $2+1$ dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work (arXiv:1308.4673), physics of a symmetry enriched phase can be extracted by the Mathematics of (hidden) quantum…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
We present a systematic framework for constructing exactly-solvable lattice models of symmetry-enriched topological (SET) phases based on an enlarged version of the string-net model. We also gauge the global symmetries of our SET models to…