Related papers: Real-space representation of the second Chern numb…
We construct, by a procedure involving a dimensional reduction from a Chern-Simons theory with borders, an effective theory for a 1+1 dimensional superconductor. 1That system can be either in an ordinary phase or in a topological one,…
We rederive the spectral asymmetry of the Wilson-Dirac model in external fields, paying attention to the Chern number due to the Berry connection. We interpret the smooth part of the spectral asymmetry as the Streda formula that is…
Local topological markers, topological invariants evaluated by local expectation values, are valuable for characterizing topological phases in materials lacking translation invariance. The Chern marker -- the Chern number expressed in terms…
An odd index theorem for higher odd Chern characters of crossed product algebras is proved. It generalizes the Noether-Gohberg-Krein index theorem. Furthermore, a local formula for the associated cyclic cocycle is provided. When applied to…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been…
We present an approach for the calculation of the $\mathbb{Z}_2$ topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline…
We extend the Yao-Kivelson decorated honeycomb lattice Kitaev model [Phys. Rev. Lett. 99,247203 (2007)] of an exactly solvable chiral spin liquid by including disordered exchange couplings. We have determined the phase diagram of this…
Higher-order topological phases and real topological phases are two emerging topics in topological states of matter, which have been attracting considerable research interest. However, it remains a challenge to find realistic materials that…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
Local markers provide an efficient and powerful characterization of topological features of many systems, especially when the translation symmetry is broken. Recently, a universal topological local marker applicable in different symmetry…
We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…
Topological states, first known as quantum Hall effect or Chern insulating crystal, have been generalized to many classical wave systems where potential applications such as robust waveguiding, quantum computing and high-performance lasers…
We study the phase transitions of three-dimensional $\mathcal{N}=2$ $U(N)$ Chern-Simons theory on $\mathbb{S}^3$ with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various…
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…
If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…
We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with…
Cold-atom experiments in optical lattices offer a versatile platform to realize various topological quantum phases. A key challenge in those experiments is to unambiguously probe the topological order. We propose a method to directly…
Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…