Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model

TL;DR

This paper explores the phase diagram of an extended honeycomb XY model, revealing the emergence of a chiral spin liquid phase driven by frustration and chiral interactions, using advanced numerical methods.

Contribution

It demonstrates the realization of the Kalmeyer-Laughlin chiral spin liquid in an extended XY model with specific interactions, combining numerical evidence and theoretical analysis.

Findings

Identification of a topologically ordered chiral spin liquid phase.

Demonstration of the CSL emergence due to small chiral perturbations.

Characterization of the phase by chiral order and entanglement spectrum.

Abstract

The frustrated XY model on the honeycomb lattice has drawn lots of attentions because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this work, we study the extended spin-$\frac{1}{2}$ XY model with nearest-neighbor ($J_1$), and next-nearest-neighbor ($J_2$) interactions in the presence of a three-spins chiral ($J_{\chi}$) term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small $J_{\chi}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a non-magnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral $SU(2)_{1}$ conformal field theory.