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

Quantum theory provides an extensive framework for the description of the equilibrium
properties of quantum matter. Yet experiments in quantum simulators have now opened up …

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 …

Topological phases constitute an exotic form of matter characterized by non-local properties
rather than local order parameters. The paradigmatic Haldane model on a hexagonal lattice …

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The
geometry of the eigenstates is encoded in the quantum geometric tensor—comprising the …

This is an introductory review of the physics of topological quantum matter with cold atoms.
Topological quantum phases, originally discovered and investigated in condensed matter …

Topological properties lie at the heart of many fascinating phenomena in solid-state systems
such as quantum Hall systems or Chern insulators. The topology of the bands can be …

Abstract Machine-learning techniques such as artificial neural networks are currently
revolutionizing many technological areas and have also proven successful in quantum …

The last years have witnessed rapid progress in the topological characterization of out-of-
equilibrium systems. We report on robust signatures of a new type of topology—the Euler …

Knots have a twisted history in quantum physics. They were abandoned as failed models of
atoms. Only much later was the connection between knot invariants and Wilson loops in …