Related papers: Classifying bulk-edge anomalies in the Dirac Hamil…
The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of…
Planar topological superconductors with power-law-decaying pairing display different kinds of topological phase transitions where quasiparticles dubbed nonlocal-massive Dirac fermions emerge. These exotic particles form through long-range…
We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and…
The conventional bulk-boundary correspondence breaks down in non-Hermitian systems. In this paper, we reestablish the bulk-boundary correspondence in one-dimensional non-Hermitian systems by applying the scattering theory, which is a…
We use the relation between certain diffeomorphisms in the bulk and Weyl transformations on the boundary to build the conformal structure of the metric in the presence of matter in the bulk. We explicitly obtain the conformal anomaly in any…
We consider the N=1 supersymmetric kink on a circle, i.e., on a finite interval with boundary or transition conditions which are locally invisible. For Majorana fermions, the single-particle Dirac Hamiltonian as a differential operator…
The Spin-Chern ($C_s$) was originally introduced on finite samples by imposing spin boundary conditions at the edges. This definition lead to confusing and contradictory statements. On one hand the original paper by Sheng and collaborators…
We consider light scattering by two dimensional arrays of high-index dielectric spheres arranged into the triangular lattice. It is demonstrated that in the case a triple degeneracy of resonant leaky modes in the Gamma-point the scattering…
Chiral anomaly modifies the scattering processes in chiral systems which can be computed using the Maxwell-Chern-Simons theory that couples electrodynamics to the pseudoscalar field $\theta$ describing the topological charge induced be…
We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of eigenfunctions…
In the AdS/CFT correspondence the boundary Ward identities are encoded in the bulk constraints. We study the three-dimensional version of this result using the Chern-Simons formulation of gravity. Due the metric boundary conditions the…
We consider massless Majorana fermion systems with $G=\mathbb{Z}_N$, $SO(N)$, and $O(N)$ symmetry in one-dimensional spacetime. In these theories, phase ambiguities of the partition functions are given as the exponential of the…
The bulk-boundary correspondence, which relates topological properties of a material in the bulk to the presence of robust modes localized on the edge, is at the core of the now mature field of topological wave physics. More recently, it…
In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac…
In this paper we discuss decomposition in the context of three-dimensional Chern-Simons theories. Specifically, we argue that a Chern-Simons theory with a gauged noneffectively-acting one-form symmetry is equivalent to a disjoint union of…
We study the Dirac quasiparticles in $d$-dimensional lattice systems of electrons in the presence of domain walls ($d=1$), vortices ($d=2$), or hedgehogs ($d=3$) of superconducting and/or insulating, order parameters, which appear as mass…
We introduce the Dirac eigenmode filtering of topological charge density associated with Ginsparg-Wilson fermions as a tool to investigate the local structure of topological charge fluctuations in QCD. The resulting framework is used to…
We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable $(d+1)$-dimensional…
The chiral central charge $c_-$ is a key topological invariant of the edge characterizing the bulk two-dimensional chiral topological order, but its direct evaluation in microscopic spin models has long been a challenge, especially for…
We investigate the dynamics of a boundary field coupled to a bulk field with a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski (Randall-Sundrum) brane. An instability criterion for the coupled boundary and bulk…