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

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.

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• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Efficient calculation of three-dimensional tensor networks
• Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Thermal Hall response of an abelian chiral spin liquid at finite temperatures
• Floquet dynamical chiral spin liquid at finite frequency
• Variational optimization of projected entangled-pair states on the triangular lattice
• Chiral Edge States Emerging on Anyon-Net