Laboratoire de Physique Théorique
Toulouse - UMR 5152

Chiral spin liquids (CSLs) are bosonic variant of fractional quantum Hall states realized in spin models. As a topologically ordered phase of matter, CSLs have degenerate ground states on torus while host chiral edge modes (or entanglement spectrum) on an open disk. As numerical confirmation of CSL ground states in spin models is still a challenging problem and conventional numerical methods have various limitations, we consider the entanglement based projected entangled pair states (PEPS) method for simulation of CSLs. Nevertheless, the application of tensor network method to CSLs is not so straightforward due to the existence of a no-go theorem.

In this talk, I will firstly introduce the background of the topological obstruction in CSLs, and then report our recent progress. (i) We extend the original bosonic PEPS framework to describe CSLs on non-bipartite lattices. (ii) We propose the fermionic PEPS ansatz based on the parton construction. The fermionic PEPS representation for CSLs provides a faithful description of chiral edge spectrum, which cures a long-standing issue in bosonic PEPS.