相关论文: Chern numbers, localisation and the bulk-edge corr…
The Chern number is often used to distinguish between different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline…
We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact…
Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the…
We investigate the topological phase transition with large Chern number in a coupled layer system. The topological transitions between different topological superfluids can be realized by controlling the binding energy, interlay tunneling…
In this paper we investigate the unbounded Kasparov product between a differentiable module and an unbounded cycle of a very general kind that includes all unbounded Kasparov modules and hence also all spectral triples. Our assumptions on…
By considering the general properties of approximate units in differentiable algebras, we are able to present a unified approach to characterising completeness of spectral metric spaces, existence of connections on modules, and the lifting…
We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov…
We study an one-dimensional transverse field Ising model with additional periodically modulated real and complex fields. It is shown that both models can be mapped on a pseudo spin system in the k space in the aid of an extended Bogoliubov…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
The study of unconventional phases and elucidation of correspondences between topological invariants and their intriguing properties are pivotal in topological physics. Here, we investigate a complex exceptional ring (CER), composed of a…
The theory of the higher Chern numbers in the presence of strong disorder is developed. Sharp quantization and homotopy invariance conditions are provided. The relevance of the result to the field of strongly disordered topological…
We report on a study of topological properties of Fibonacci quasicrystals. Chern numbers which label the dense set of spectral gaps, are shown to be related to the underlying palindromic symmetry. Topological and spectral features are…
Topological phases with broken time-reversal symmetry and Chern number |C|>=2 are of fundamental interest, but it remains unclear how to engineer the desired topological Hamiltonian within the paradigm of spin-orbit-coupled particles…
The valley-Chern and spin-valley-Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which…
Two recent papers proved that complex index pairings can be calculated as the half-signature of a finite dimensional matrix, called the spectral localizer. This paper contains a new proof of this connection for even index pairings based on…
In this paper, we formulate the real-space Chern number in a supercell framework. In this framework, the overlap matrix between two corners of the Brillouin zone (BZ) is derived from diagonalizing the real-space Hamiltonian with periodic…
Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vector bundles is established, which makes some progress towards…
We present a definition of indefinite Kasparov modules, a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov module we…