Topological Order in Spin Liquids with Chirality

Burkhard Scharfenberger

Published Jan 1, 2011• 0 citations

Abstract

We use the Kalmeyer-Laughlin Chiral Spin Liquid as building block to construct a hierarchy of higher-spin spin liquids and determine numerically their topological properties. We compute the entanglement spectra of some of these liquids as well as of ground states of critically frustrated quantum magnets. From the comparison, we find preliminary evidence for a topological phase transition in these systems.

DOI: 10.5445/ir/1000023742

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Topological Order in Spin Liquids with Chirality

Burkhard Scharfenberger

Published Jan 1, 2011• 0 citations

Publisher

Abstract

DOI: 10.5445/ir/1000023742

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\text{SU}{(2)}_{1}

chiral spin liquid emerges in the highly frustrated region, which is unambiguously identified by two topologically degenerate ground states, a modular matrix, and characteristic level counting in an entanglement spectrum, featuring the same topological order of the $\ensuremath{\nu}=1/2$ bosonic Laughlin state. The phase boundaries among the different orders are determined by the energy level crossing analysis and wave-function fidelity susceptibility.

\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 $({J}_{\ensuremath{\chi}})$ 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 ${J}_{\ensuremath{\chi}}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a nonmagnetic 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.

\text{XY}

model when Rydberg atoms are arranged in a breathing kagome lattice. Using the infinite density matrix renormalization group, we numerically calculate the ground state's chiral order parameter, spin-spin correlations, Chern number, and entanglement spectrum. Our numerical results provide strong evidence for the chiral spin liquid phase. Furthermore, we identify a quantum phase transition from a Dirac spin liquid to a chiral spin liquid as the lattice geometry is tuned from the isotropic kagome to the breathing kagome lattice.