Topological photonics is a rapidly emerging field of research in which geometrical and
topological ideas are exploited to design and control the behavior of light. Drawing …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

Since the discovery of topological insulators, many topological phases have been predicted
and realized in a range of different systems, providing both fascinating physics and exciting …

Recent experimental developments in diverse areas—ranging from cold atomic gases to
light-driven semiconductors to microcavity arrays—move systems into the focus which are …

Non-Hermiticity gives rise to unique topological phases that have no counterparts in
Hermitian systems. Such intrinsic non-Hermitian topological phases appear even in one …

In this article we provide a review of geometrical methods employed in the analysis of
quantum phase transitions and non-equilibrium dissipative phase transitions. After a …

Recently, the search for topological states of matter has turned to non-Hermitian systems,
which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices …

We uncover a topological classification applicable to open fermionic systems governed by a
general class of Lindblad master equations. These “quadratic Lindbladians” can be …

We present a framework to systematically address topological phases when finer
partitionings of bands are taken into account, rather than only considering the two …

We present a full symmetry classification of fermion matter in and out of thermal equilibrium.
Our approach starts from first principles, the ten different classes of linear and antilinear state …