Related papers: Multicolor groups for molecules and solids
The spatial symmetry of matter - including finite objects like molecules or atomic clusters, and extended objects like periodic or aperiodic crystals - is described using point groups and space groups. Magnetic point groups and space groups…
Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles to condensed matter systems. Here, by combining symmetry analysis and tight-binding model calculations, we elucidate…
The recent discovery of altermagnets has opened new perspectives in the field of ordered phases in condensed matter. In strongly-correlated superfluids, the nodal p-wave and d-wave ordered phases of $^{3}$He and cuprates play a prominent…
Lattice color groups are introduced and used to study the partitioning of a periodically- or quasiperiodically-ordered set of points into N symmetry-related subsets. Applications range from magnetic structure to superlattice ordering in…
Altermagnetism, recently spotlighted in condensed matter physics, presents captivating physical properties and holds promise for spintronics applications. This study delves into the theoretical description and categorization of…
The concept of spin symmetries has gained renewed interest as a valuable tool for classifying unconventional magnetic phases, including altermagnets and recently identified p-wave magnets. In this work, we show that in compounds with weak…
Molecular magnets have received significant attention because of their potential applications in quantum information and quantum computing. A delicate balance of electron correlation, spin-orbit coupling (SOC), ligand field splitting, and…
The synthesis of molecular magnets has undergone rapid progress in recent years. Each of the identical molecular units can contain as few as two and up to several dozens of paramagnetic ions (spins). Although these materials appear as…
Compact quantum groups can be studied by investigating their co-representation categories in analogy to the Schur-Weyl/Tannaka-Krein approach. For the special class of (unitary) "easy" quantum groups these categories arise from a…
Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of…
Group theoretical methods are used to determine the electromagnetic properties of artificial magnetic meta-materials, based solely upon the symmetries of the underlying constituent particles. Point groups for such materials are determined.…
A submodule of a $\mathbb{Z}$-module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a $\mathbb{Z}$-module, the group formed by the symmetries of the…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
Spin space groups (SSGs) impose fundamentally different constraints on magnetic configurations in real and reciprocal spaces. As a consequence, the correspondence between real-space and momentum-space spin arrangements is far richer than…
For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has…
Altermagnets host an array of magnetic multipoles, which are often visualized and studied in the reciprocal space. In the real space, the relative phase of the multipoles of the spin-density around atoms determines whether a system is an…
This paper presents two facets. First, we show that the periodic table of chemical elements can be described, understood and modified (as far as its format is concerned) on the basis of group theory and more specifically by using the group…
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…
The multipole moment is an established concept of electrons in solids. Entanglement of spin, orbital, and sublattice degrees of freedom is described by the multipole moment, and spontaneous multipole order is a ubiquitous phenomenon in…
Metal-organic frameworks (MOFs) are a highly tunable class of crystalline materials where metal atoms or clusters are connected by organic linkers. They offer a versatile platform for exploring quantum phenomena such as entangled magnetism,…