Speaker
Description
The Landau paradigm has been highly successful in understanding and classifying phases of matter through symmetry breaking and local order parameters. However, some quantum phases cannot be fully characterized within this framework, as their defining properties are topological rather than local. A paradigmatic example is the fractional quantum Hall effect, a strongly correlated phase where topology and interactions lead to exotic properties, such as quasiparticles carrying fractional charge and obeying neither bosonic nor fermionic statistics.
In this talk, I will use the fractional quantum Hall effect as an example to introduce topological phases. I will then present the Bose–Hofstadter model, a two-dimensional lattice system of interacting bosons exhibiting fractional quantum Hall physics. Finally, I will discuss how we can study such quantum many-body systems numerically, in particular how neural networks can be used as variational wave functions to approximate their ground states, with an emphasis on the Bose-Hofstadter case.