Related papers: Topological state evolution by symmetry-breaking

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in solid-state materials. Topological quantum chemistry has…

We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to…

A hallmark feature of topologically ordered states of matter is the dependence of ground state degeneracy (GSD) on the topology of the manifold determined by the global shape of the system. Although the topology of a physical system is…

Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…

We derive the full spectrum of decorated Cayley trees that constitute tree analogs of selected two-dimensional Euclidean lattices; namely of the Lieb, the double Lieb, the kagome, and the star lattice. The common feature of these Euclidean…

We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition…

Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real…

The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…

We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…

Recent realizations of exotic topological states in condensed matter and cold atoms have advanced the exploration for topological characteristics, such as invariant topological orders and band inversion. Here we construct a 1D optical…

Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…

Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…

In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…

Topological materials ranging from topological insulators to semimetals host many novel quantum phenomena including quantum spin Hall effect and topological Fermi arcs. Transitions between these topological phases have attracted much…

While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform…

The search for topological systems has recently broadened to include random substitutional alloys, which lack the specific crystalline symmetries that protect topological phases, raising the question whether topological properties can be…

Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…

Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…

A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for…

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…