Related papers: Modular transformations and topological orders in …
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…
Because global topological properties are robust against local perturbations, understanding and manipulating the topological properties of physical systems is essential in advancing quantum science and technology. For quantum computation,…
Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been…
In an ordinary three-dimensional metal the Fermi surface forms a two-dimensional closed sheet separating the filled from the empty states. Topological semimetals, on the other hand, can exhibit protected one-dimensional Fermi lines or…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer information than the bulk degeneracy.…
To date, almost all of the discussions on topological insulators (TIs) have focused on two- and three-dimensional systems. One-dimensional (1D) TIs manifested in real materials, in which localized spin states may exist at the end or near…
Quantum rings have emerged as a playground for quantum mechanics and topological physics, with promising technological applications. Experimentally realizable quantum rings, albeit at the scale of a few nanometers, are 3D nanostructures.…
We further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced in Phys. Rev. Lett. 108, 036803 (2012). We show how, in the presence of time-reversal symmetry, Z_2 invariants that distinguish…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…
Beyond the well-known topological band theory for single-particle systems, it is a great challenge to characterize the topological nature of interacting multi-particle quantum systems. Here, we uncover the relation between topological…
A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an…
We discuss systems which have some, but not all of the hallmarks of topological phases. These systems' topological character is not fully captured by a local order parameter, but they are also not fully described at low energies by…
We address the problem of identifying a 2+1d topologically ordered phase using measurements on the ground-state wavefunction. For non-chiral topological order, we describe a series of bulk multipartite entanglement measures that extract the…
We present a general method to analyze the topological nature of the domain boundary connectivity that appeared in relaxed moir\'e superlattice patterns at the interface of 2-dimensional (2D) van der Waals (vdW) materials. At large enough…
The vast majority of symmetry-protected topological (SPT) states are difficult to detect, which often leads to their misidentification as ordinary or topologically trivial phases. In this work, we propose a general framework for detecting…
The spin-orbit coupling field, an atomic magnetic field inside a Kramer's system, or discrete symmetries can create a topological torus in the Brillouin Zone and provide protected edge or surface states, which can contain relativistic…
We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular…
We develop a method to characterize topological phase transitions for strongly correlated Hamiltonians defined on two-dimensional lattices based on the many-body Berry curvature. Our goal is to identify a class of quantum critical points…