Related papers: Revealing Chern number from quantum metric
Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where…
Valley photonics has emerged as a promising platform in topological photonic systems, yet the topological nature of valley-dependent phenomena remains unsettled. Theoretically, inter-valley scattering may occur with structural…
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of…
Chern insulator is a building block of many topological quantum matters, ranging from quantum spin Hall insulators to fractional Chern insulators. Here, we discuss a new type of insulator, which consists of two half filled ordinary Chern…
The orbital magnetic susceptibility of an electron gas in a periodic potential depends not only on the zero field energy spectrum but also on the geometric structure of cell-periodic Bloch states which encodes interband effects. In addition…
A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…
This lecture note adresses the correspondence between spectral flows, often associated to unidirectional modes, and Chern numbers associated to degeneracy points. The notions of topological indices (Chern numbers, analytical indices) are…
The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical…
We propose a scheme for measuring topological properties in a two-photon-driven Kerr-nonlinear resonator (KNR) subjected to a single-photon modulation. The topological properties are revealed through the observation of the Berry curvature…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
The geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the curvature of the Berry connection. We present a…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
In 2D Chern insulators (2D CI), the topology of the bulk states is captured by a topological invariant, the Chern number. The scalar bulk-boundary correspondence (sBBC) relates the change in Chern number across an interface with the number…
We study the Riemannian metric and the Euler characteristic number of the Bloch band in a 1D spin model with multi-site spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the…
We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse…
The geometric interpretation of (pseudo)spin 1/2 systems on the Bloch sphere has been appreciated across different areas ranging from condensed matter to quantum information and high energy physics. Although similar notions for larger…
Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the…
In this work, we study the deformation of Hermitian metrics with Chern connection. By adapting the conformal perturbation method of Aubin and Ehrlich to Hermitian setting, we prove that Hermitian metrics with quasi-positive (resp.…
The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements. Recently, it was predicted that topology can also give rise to a…
We report on a study of topological properties of Fibonacci quasicrystals. Chern numbers which label the dense set of spectral gaps, are shown to be related to the underlying palindromic symmetry. Topological and spectral features are…