Related papers: Two-Dimensional Space-Time Groups: Classification …
Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in $D+1$…
Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
Wigner's seminal work on the Poincar\'e group revealed one of the fundamental principles of quantum theory: symmetry groups are projectively represented. The condensed-matter counterparts of the Poincar\'e group could be the spacetime…
Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
This paper presents a space-time-wise orthogonal analysis of space-time crystals. This analysis provides a solution consisting of a pair of explicit parametric equations that result from a separate application of the Bloch-Floquet theorem…
Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the…
The public and scientists constantly have different perspectives. While on a time crystal, they stand in line and ask: What is a time crystal? Show me a material that is spontaneously crystalline in time? This study synthesizes a photonic…
The traditional systems researched in condensed matter physics always have spatial translation symmetry. However for space-time crystal systems, the spatial translation symmetry is no longer preserved and the lattice potential have…
The wide-range application of photonic crystals and metamaterials benefits from the enormous design space of three-dimensional sub-wavelength structures. In this work, we study the space group constraints on photonic dispersions for all 230…
Crystals are the foundation of numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods seldom consider the space group constraint which is crucial…
The symmetry of a crystal structure with a three-dimensional (3D) lattice can be classified by one of the 230 space group types. For some types of crystals, e.g. crystalline films, surfaces, or planar interfaces, it is more appropriate to…
Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other…
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…
Time is, figuratively and literally, becoming the new dimension for crystalline matter. As such, rapid recent progress on time-varying media gave rise to the notion of temporal and spatiotemporal crystals. Fundamentally rethinking the role…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
As a fundamental concept of all crystals, space groups are partitioned into symmorphic groups and nonsymmorphic groups. Each nonsymmorphic group contains glide reflections or screw rotations with fractional lattice translations, which are…
Crystallographic groups are conventionally studied in real space to characterize crystal symmetries. Recent work has recognized that when these symmetries are realized projectively, momentum space inherently accommodates nonsymmorphic…
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…