Related papers: On the Bott index of unitary matrices on a finite …
The Bott index of two unitary operators on an infinite dimensional Hilbert space is defined. homotopic invariance with respect to multiplicative unitary perturbations of the type identity plus trace class and the "logarithmic" law for the…
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual…
The Bott index has become an indispensable tool to probe the topology of quantum matter, particularly in systems lacking translational symmetry. Constructed from a plaquette operator, it retains the phase information while discarding the…
We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…
The Bott index is inherently global. The pseudospectal index is inherently local, and so now the preferred name is the localizer index. We look at these on a rather standard model for a Chern insulator, with an emphasis how to program these…
Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two period-two and four period-eight cycles,…
In 1956, Bott in his celebrated paper on closed geodesics and Sturm intersection theory, proved an Index Iteration Formula for closed geodesics on Riemannian manifolds. Some years later, Ekeland improved this formula in the case of convex…
We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under…
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…
This paper is a survey of the $\mathbb{Z}_2$-valued invariant of topological insulators used in condensed matter physics. The $\mathbb{Z}$-valued topological invariant, which was originally called the TKNN invariant in physics, has now been…
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…
We investigate the role of disorder on the various topological magnonic phases present in deformed honeycomb ferromagnets. To this end, we introduce a bosonic Bott index to characterize the topology of magnon spectra in finite, disordered…
Cold atoms confined in periodic potentials are remarkably versatile quantum systems for implementing simple models prevalent in condensed matter theory. In the current experiment, we realize the 2D Bose-Hubbard model by loading a…
Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological…
Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible…
We explicitly construct a pair of immersed tori in three dimensional Euclidean space that are related by a mean curvature preserving isometry. These Bonnet pair tori are the first examples of compact Bonnet pairs. This resolves a…
A $U(1)$ gauge theory coupled to a Wilson fermion on a $2+1$ dimensional cubic lattice is known to exhibit Chern insulator like topological transitions as a function of the the ratio $M/R$ where $M$ is the fermion mass and $R$ is the Wilson…
Thermal noise can destroy topological insulators (TI). However we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian,…
Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and the research interest in the non-Euclidean generalization of topological phenomena, we investigate the Chern insulator phases in…
We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator…