Chiral Tensor Networks Workshop: Report

The IQTN Workshop on Chiral Tensor Networks brought together a group of 22 experts from 9 countries at Cosener’s House, Abingdon, from Dec 12-14, 2023, with the goal to advance on the theoretical understanding and the development of numerical algorithms for the representation of chiral topological phases of matter in two dimensions.

Following on from three overview talks and eight more specialised research talks, the workshop fostered lively discussions of some of the most challenging questions probing the representational power of tensor networks for chiral phases. The results presented at the workshop gave a clear account of the success of PEPS in characterising chiral phases. The most recent numerical results clearly demonstrate that PEPS can capture the short-distance correlations perfectly. However, at long distances these correlations have an algebraic tail. While this phenomenon is understood analytically for the case of free theories, it remains a purely empirical finding in interacting theories. Participants identified a list of open questions, remaining challenges, and desirable future developments, which are documented on the conference webpages. Examples include progress on an analytical understanding of interacting chiral PEPS, decoding the role of chiral properties at the level of individual tensors, and the development of tensor network approaches for the description of fractional Chern insulator phases in realistic materials, to allow the modelling of recently discovered twisted multilayer dichalcogenides hosting such states. Slides from most presentations are available via the conference website.

Plans for a follow-on meeting to tentatively take place at the University of Zürich have already been made.