Related papers: Robustness of the Spin-Chern number
A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The…
A Chern band is characterized by a Wannier obstruction indicating the absence of a basis of complete, orthogonal, and exponentially-localized states. Here, we study the properties of real space bases of a Chern band obtained by relaxing…
We show by example that the Chern numbers c_1^3 and c_1 c_2 of a complex 3-fold are not determined by the topology of the underlying smooth compact 6-manifold. In fact, we observe that infinitely many different values of a Chern number can…
Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant…
For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity.…
We study on-shell scattering amplitudes for continuous-spin particles (CSPs). Poincar\'e invariance, little-group $ISO(2)$ covariance, analyticity, and on-shell factorisation (unitarity) impose stringent conditions on these amplitudes. We…
We use constructive bounded Kasparov K-theory to investigate the numerical invariants stemming from the internal Kasparov products $K_i(\mathcal A) \times KK^i(\mathcal A, \mathcal B) \rightarrow K_0(\mathcal B) \rightarrow \mathbb R$,…
Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to…
In this thesis Chern-Simons theories based on Lie algebras with invariant metric are constructed. It is discussed how contractions lead systematically to (higher spin) kinematical algebras of, e.g., Poincar\'e, Galilei and Carroll type and…
Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
Topological invariants, including the Chern numbers, can topologically classify parameterized Hamiltonians. We find that topological invariants can be properly defined and calculated even if the parameter space is discrete, which is done by…
The discovery of quantum spin Hall effect has ignited the field of topological physics with vast variety of exotic properties. Here, we present the emergence of doubled quantum spin Hall effect in two dimensions characterized with a high…
Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in…
Chern numbers are gaining traction as they characterize topological phases in various physical systems. However, the resilience of the system topology to external perturbations makes it challenging to experimentally investigate transitions…
Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
Nodal superconductors without inversion symmetry exhibit nontrivial topological properties, manifested by topologically protected flat-band edge states. Here we study the effects of breaking translational symmetry, crucial to the definition…