Chiral spin liquids on the kagome lattice with projected entangled simplex states

TL;DR

This paper demonstrates that the infinite projected entangled simplex state (iPESS) tensor network can accurately represent chiral spin liquids on the kagome lattice, revealing their entanglement structure and phase transition properties.

Contribution

The authors extend iPESS tensor network methods to faithfully model chiral spin liquids on the kagome lattice, including the construction of a chiral ansatz breaking certain symmetries.

Findings

iPESS captures the chiral gapless entanglement spectrum with SU(2)_1 conformal field theory

Correlation functions show long-range tail consistent with bulk-edge correspondence

Identification of a non-chiral manifold with an emergent tensor conservation law

Abstract

The infinite projected entangled simplex state (iPESS), a type of tensor network (TN) state, has been used successfully for simulating and characterizing {\it non-chiral} spin liquids on the kagome lattice. Here, we demonstrate that iPESS also provides a faithful representation of a {\it chiral} spin liquid (CSL) on the same lattice, namely the ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet with a scalar chirality. By classifying local tensors according to SU$(2)$ and point group symmetries, we construct a chiral ansatz breaking reflection $P$ and time reversal $T$ symmetries while preserving $PT$. The variational TN states are shown to host, for bond dimension $D\ge 8$, a chiral gapless entanglement spectrum following SU$(2)_1$ conformal field theory. The correlation function shows a small weight long-range tail complying with the prediction of the TN bulk-edge correspondence. %{\color{red}With more constraints included, the chiral ansatz is reduced to a non-chiral one which preserves full point group symmetries due to an emergent {\it tensor conservation law} and is of relevance to the ground state at the Heisenberg point. Lastly, by simulations in the complete ansatz family we discuss the transition from the non-chiral spin liquid to the CSL induced by the scalar chirality term.} We identify a non-chiral manifold spanned by only a subset of symmetric tensors where a new emergent {\it tensor conservation law} is realized. This allows us to both probe the stability of the non-chiral spin liquid and discuss its transition to CSL induced by a scalar chirality term.