SU(2)$_1$ chiral edge modes of a critical spin liquid

TL;DR

This paper analyzes chiral edge modes in a family of PEPS-based spin liquid states, showing they are described by a chiral SU(2)$_1$ CFT, indicating a critical bulk and potential boundary between topological and trivial phases.

Contribution

It provides a detailed analysis of edge modes in PEPS-derived chiral spin liquids, revealing their description by a chiral SU(2)$_1$ conformal field theory and suggesting a critical bulk with emergent U(1) symmetry.

Findings

Edge modes are well described by chiral SU(2)$_1$ CFT.

Bulk appears critical with emergent U(1) gauge symmetry.

Potential boundary between chiral topological and trivial phases.

Abstract

Protected chiral edge modes are a well-known signature of topologically ordered phases like the Fractional Quantum Hall States. Recently, using the framework of projected entangled pair states (PEPS) on the square lattice, we constructed a family of chiral Resonating Valence Bond states with $\mathbb{Z}_2$ gauge symmetry. Here we revisit and analyze in full details the properties of the edge modes as given by their Entanglement Spectra on a cylinder. Surprisingly, we show that the latter can be well described by a chiral SU(2)$_1$ Conformal Field Theory (CFT), as for the $\nu=1/2$ (bosonic) gapped Laughlin state, although our numerical data suggest a critical bulk compatible with an emergent $U(1)$ gauge symmetry. We propose that our family of PEPS may physically describe a boundary between a chiral topological phase and a trivial phase.