Chiral topological spin liquids with projected entangled pair states

TL;DR

This paper constructs chiral topological spin liquids on a square lattice using PEPS, revealing their topological sectors, correlation properties, and chiral edge modes consistent with conformal field theory predictions.

Contribution

It introduces a family of chiral spin liquids with $d+i d$ symmetry using PEPS, analyzing their topological sectors, correlations, and entanglement properties.

Findings

Four topological sectors on a cylinder with orthogonal states in the infinite limit

Evidence of short-range triplet and long-range singlet correlations

Chiral edge modes in the entanglement spectrum matching conformal field theory predictions

Abstract

Topological chiral phases are ubiquitous in the physics of the Fractional Quantum Hall Effect. Non-chiral topological spin liquids are also well known. Here, using the framework of projected entangled pair states (PEPS), we construct a family of chiral spin liquids on the square lattice which are generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from deformed local tensors with $d+i\, d$ symmetry. On a cylinder, we construct four topological sectors with even or odd number of spinons on the boundary and even or odd number of ($\mathbb{Z}_2$) fluxes penetrating the cylinder which, we argue, remain orthogonal in the limit of infinite perimeter. The analysis of the transfer matrix provides evidence of short-range (long-range) triplet (singlet) correlations as for the critical (non-chiral) RVB state. The Entanglement Spectrum exhibits chiral edge modes, which we confront to predictions of Conformal Field Theory, and the corresponding Entanglement Hamiltonian is shown to be long ranged.