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

The central idea of this review is to consider quantum field theory models relevant for
particle physics and replace the fermionic matter in these models by a bosonic one. This is …

Lattice gauge theories, which originated from particle physics in the context of Quantum
Chromodynamics (QCD), provide an important intellectual stimulus to further develop …

In the field of quantum simulation of condensed matter phenomena by artificially
engineering the Hamiltonian of an atomic, molecular or optical system, the concept of …

Certain lattice wave systems in translationally invariant settings have one or more spectral
bands that are strictly flat or independent of momentum in the tight binding approximation …

The discovery of the quantum spin Hall effect and topological insulators more than a decade
ago has revolutionized modern condensed matter physics. Today, the field of topological …

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 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 …

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying
quantum field theories, and has led to impressive achievements. In particular, it significantly …

Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great
interest in different areas of physics. AB caging can be harnessed to explore the rich and …