Fractional Quantum Anomalous Hall Effect and
Fractional Chern Insulators

The international workshop FQAH24 took place from February 5 - 8, 2024. There were 76 participants from 16 countries. The aim of the workshop was to bring together scientists working in various aspects of the fractional quantum Hall effect and its experimental realization in engineered moiré materials, highlighting the progress and prospects for the recent experimental breakthrough on the quantized fractional Hall resistance at zero magnetic field.

The workshop included speakers from various sub-areas and covered both theory and experiment. For example, in the area of the fractional quantum anomalous Hall effect and moiré materials, Long Ju gave an opening lecture reviewing the recent development of realizing correlated and topological states in moiré systems, and presented his experimental work on the fractional quantum anomalous Hall effect in pentalayer-graphene. Xiaodong Xu gave a colloquium talk on his journey of realizing the fractional quantum anomalous Hall effect in twisted MoTe2, from the optical signature to the final evidence in transport experiments. Tingxin Li reported the observation of integer and fractional quantum anomalous Hall effects in 2D semiconductor moiré superlattices.
Several speakers, for example Bogdan A. Bernevig, Kai Sun, and Nicolas Regnault, focused on the theory of fractional Chern insulators in moiré materials. Some talks, such as those by Andreas Läuchli, Steven H. Simon, and Oskar Vafek, discussed correlated phases beyond fractional Chern insulators in moiré materials. On the transport theory, examples were Sankar Das Sarma on analyzing quantum anomalous Hall effect experiments in the context of the conventional quantum Hall effect, and Ady Stern on composite Fermi liquids in half filled Chern bands. In the area of ab initio simulation of large scale systems, Jeil Jung and Jianpeng Liu talked about modelling of pentalayer-graphene, and Di Xiao and Ting Cao gave presentations on the machine learning force field applied to twisted WSe2 and MoTe2. There were also talks about the bosonic fractional quantum Hall effect, such as those from Ruirui Du on the bosonic Laughlin state in a moat band without magnetic field, and from Nathan Goldman on the strongly-correlated topological matter with quantum gases. In the closing remark, Emil Bergholtz listed several key open questions in the field of the fractional quantum anomalous Hall effect and fractional Chern insulators, the break-throughs on which are highly demanded. Overall, the talks in this workshop demonstrated the state-of-the-art in the field.

The contributions from young scientists are very important for the progress of the field. Several invited talks in this workshop were given by speakers who had recently obtained faculty positions, including Yonglong Xie, Trithep Devakul and Jie Wang. There were also two poster sessions on the first two days of the workshop. Thirty participants, most of whom are PhD students and postdocs, contributed poster presentations which led to high attendance.
The organizers are happy to see that this workshop brought people working on the quantum Hall effect, two-dimensional materials, cold atoms, and ab initio simulation together and led to fruitful discussions. It was clear that the participants from different communities united under a common keen interest on the fractional quantum anomalous Hall effect and fractional Chern insulators. From the positive feedback by many participants, the organizers are confident that this event provided an excellent platform to exchange ideas, identify key scientific problems, and initiate collaborations, which will keep the research field flourish in the future.