Quantum circuits—built from local unitary gates and local measurements—are a new
playground for quantum many-body physics and a tractable setting to explore universal …

A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

The past decades have witnessed an explosion of interest in topological materials, and a lot
of mathematical concepts have been introduced in condensed matter physics. Among them …

We study the Hatano-Nelson model, ie, a one-dimensional non-Hermitian chain of spinless
fermions with nearest-neighbor nonreciprocal hop**, in the presence of repulsive nearest …

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

Recent years have seen remarkable development in open quantum systems effectively
described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological …

Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

We define dynamical universality classes for many-body systems whose unitary evolution is
punctuated by projective measurements. In cases where such measurements occur …

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of
different partitions of a quantum system provides a way to probe its entanglement structure …