Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths …
Gauge theories form the theoretical foundation of our understanding of many fields of science, in particular elementary particle physics and nuclear physics. They are, however, extremely difficult to treat with conventional methods such as analytical …
Recent advancements in fabrication techniques have enabled unprecedented clean interfaces and gate tunability in semiconductor-superconductor heterostructures. Inspired by these developments, we propose protocols to realize Thouless quantum pumping …
The topological $\theta$-angle is central to the understanding of a plethora of phenomena in condensed matter and high-energy physics such as the strong CP problem, dynamical quantum topological phase transitions, and the confinement--deconfinement …
We address routing of classical and quantum information over quantum network and show how to exploit chirality (directionality) to achieve nearly optimal and robust transport. In particular, we prove how continuous-time chiral quantum walks over a …
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects, indicate …
We propose a simple scheme for tomography of band-insulating states in one- and two-dimensional optical lattices with two sublattice states. In particular, the scheme maps out the Berry curvature in the entire Brillouin zone and extracts topological …