Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice

Abstract

To study exotic excitations described by parafermions in the possible spin liquid states of SU($n$) spin systems, we introduce a parafermion parton approach. The SU($n$) spin operators can be represented by clock and shift matrices, which are shown to be the polynomials of parafermion operators in the parafermion representation. We find that SU($n$) spins can be decomposed into $n$ parafermion matrices of degree one. In this decomposition, the spin has a $\{⨂\mathrm{SU}(n){\}}^{n-1}$ gauge symmetry. As an application, we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory, both of them have been proved to be related to parafermion excitations. We find that with the symmetries of translations, $6$-fold rotation and combination of parity and time reversal, there are $9$ types and $102$ solutions for two-dimensional $Z_3$ parafermion spin liquids on the honeycomb lattice. On the contrast, there are $9$ types and $36$ solutions if both parity and time-reversal symmetries are present. Our results provide a novel route for the systematic search of new types of spin liquids with exotic anyon excitations.

13 pages, 1 figures

References in corpus (25)

• Non-Abelian Anyons and Topological Quantum Computation
• A one-dimensional liquid of fermions with tunable spin
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• An exact chiral spin liquid with non-Abelian anyons
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional topological superconductors with fractionalized Majorana fermions
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• A $\Gamma$-matrix generalization of the Kitaev model
• Parafermionic conformal field theory on the lattice
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Quantum Phase Transition in the SU(4) Spin-Orbital Model on the Triangular Lattice
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Generalized Kitaev Models and Slave Genons
• Fermionic theory for quantum antiferromagnets with spin S > 1/2
• Reflection Positivity for Parafermions
• $Z_3$ generalization of the Kitaev's spin-1/2 model

Cited by in corpus (2)

• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry