Related papers: Robustness of the Spin-Chern number
Solid state systems with time reversal symmetry and/or particle-hole symmetry often only have $\mathbb{Z}_2$-valued strong invariants for which no general local formula is known. For physically relevant values of the parameters, there may…
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,…
Solitons formed through the one-dimensional mass-kink mechanism on the edges of two-dimensional systems with non-trivial topology play an important role in the emergence of higher-order (HO) topological phases. In this connection, the…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
We investigate a model of Dirac fermions with Haldane type mass impurities which open a global topological gap even in the dilute limit. Surprisingly, we find that the chirality of this mass term, i.e., the sign of the Chern number, can be…
We compute the nonlinear development of the instabilities in C-shocks first described by Wardle, using a version of the ZEUS code modified to include a semi-implicit treatment of ambipolar diffusion. We find that, in three dimensions, thin…
The abelian Chern-Simons theory is considered on a cylindrical spacetime $\mathbb{R} \times D$, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a…
Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…
In 1994, Witten has defined a monopole invariant and he has shown the equivalence of this invariant with Donaldson's polynomial using his result in \( \SS \)-duality. This new invariant is very powerful because the gauge group is abelian.…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
Both the Haldane spin-$1$ chain and dimerized chains of spin-$1/2$ exhibit topologically protected edge states that are robust against specific perturbations. Recently, such spin chains have been specifically assembled on surfaces and we…
This thesis investigates parametrized quantum spin systems in the thermodynamic limit from a $C^*$-algebraic point of view. Our main physical result is the construction of a phase invariant for one-dimensional quantum spin chains…
The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or $SU(N)$ connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the…
We show that wavefunctions in a two-dimensional (2D) electron system with spin-orbit coupling can be characterized by a topological quantity--the Chern integer due to the existence of the intrinsic Kramers degeneracy. The…
Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have non-trivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a…
Using the Dirac and the Yang monopole in spinor condensates as examples, we show that interactions can stretch the point singularity of a monopole into an extended manifold, whose shape is strongly influenced by the sign of interaction. The…
In the field of topological insulators, the topological properties of quantum states in samples with simple geometries, such as a cylinder or a ribbon, have been classified and understood during the last decade. Here, we extend these…
In condensed matter physics, symmetry profoundly governs the fundamentals of topological matter. The emergence of new topological phase is typically linked to the enrichment of symmetries. Different parity-time symmetry relations…
Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the…
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been…