Quantum Geometric Tensor in PT\mathcal{PT}-Symmetric Quantum Mechanics

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{PT}$-symmetry breaking in $\mathcal{PT}$-symmetric systems.Comment: main text of 5 pages, plus supplementary material of 8 page

Non-Hermitian Floquet Topological Matter -- A Review

Non-Hermitian Floquet topological phases appear in systems described by time-periodic non-Hermitian Hamiltonians. This review presents a sum-up of our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. After a brief overview of the literature, we introduce our theoretical framework for the study of non-Hermitian Floquet systems and the topological characterization of non-Hermitian Floquet bands. Based on our theories, we describe typical examples of non-Hermitian Floquet topological insulators, superconductors and quasicrystals with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties and localization transitions. We conclude this review by summarizing our main discoveries and discussing potential future directions.Comment: 86 pages, 10 figures, comments are welcom