Related papers: Many-body multipole index and bulk-boundary corres…
The modern theory of polarization establishes the bulk-boundary correspondence for the bulk polarization. In this paper, we attempt to extend it to a sum rule of the bulk quadrupole moment by employing a many-body operator introduced in…
We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped…
We extend the previously defined many-body marker for two-dimensional $\mathbb{Z}_2$ topological insulators [I. Gilardoni {\it et al.}, Phys. Rev. B {\bf 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators…
We investigate higher-order topological insulators protected by chiral and anticommuting mirror symmetries. Using models in the BDI class, which include the prototypical topological quadrupole insulator, we show that breaking mirror…
Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the…
The multipole moments are fundamental properties of insulators, and have attracted lots of attention with emerging of the higher-order topological insulators. A couple of ways, including generalization of the formula for the polarization…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…
This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.
We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential…
We present a method for deriving bulk and edge invariants for interacting, many-body localized Floquet systems in two spatial dimensions. This method is based on a general mathematical object which we call a flow. As an application of our…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
We study bulk-boundary correspondences and related surface phenomena stabilized by the second Chern number in three-dimensional insulators driven in adiabatic cycles. Magnetic fields and disorder effects are incorporated in our analysis…
We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear…
The exact solution of the interacting many-body system is important and is difficult to solve. In this paper, we introduce a group method to solve the interacting many-body problem using the relation between the permutation group and the…
One-body multipole operators are defined as irreducible representations of rotational symmetry together with spatial-inversion and time-reversal symmetries, providing a systematic framework for classifying electronic internal degrees of…
We propose an index for pairs of a unitary map and a clustering state on many-body quantum systems. We require the map to conserve an integer-valued charge and to leave the state, e.g. a gapped ground state, invariant. This index is…
We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body…
We present examples in three symmetry classes of topological insulators in one or two dimensions where the proof of the bulk-edge correspondence is particularly simple. This serves to illustrate the mechanism behind the bulk-edge principle…