Chiral spin liquids on the kagome lattice with projected entangled simplex states
Sen Niu, Juraj Hašík, Ji-Yao Chen, Didier Poilblanc
Abstract
The infinite projected entangled simplex state (iPESS), a type of tensor network (TN) state, has been used successfully for simulating and characterizing nonchiral spin liquids on the kagome lattice. Here, we demonstrate that iPESS also provides a faithful representation of a 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 $\mathrm{SU}(2)$ 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 $D\ensuremath{\ge}8$, a chiral gapless entanglement spectrum following $\mathrm{SU}{(2)}_{1}$ conformal field theory. The correlation function shows a small weight long-range tail complying with the prediction of the TN bulk-edge correspondence. We identify a nonchiral manifold spanned by only a subset of symmetric tensors where a new emergent tensor conservation law is realized. This allows us to both probe the stability of the nonchiral spin liquid and discuss its transition to CSL induced by a scalar chirality term.