Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories

Abstract

Projective symmetry groups (PSG) are the mathematical tools which allow to list and classify mean-field spin liquids (SL) based on a parton construction. The seminal work of Wen and its subsequent extension to bosons by Wang and Vishwanath concerned the so-called symmetric SL: i.e. states that break neither lattice symmetries nor time reversal invariance. Here we generalize this approach to chiral (time reversal symmetry breaking) SL described in a Schwinger boson mean-field approach. A special emphasis is put on frustrated lattices (triangular and kagome lattices), where the possibility of a chiral SL ground state has recently been discussed. The PSG approach is detailed for the triangular lattice case. Results for other lattices are given in the appendices. The physical significance of gauge invariant quantities called fluxes is discussed both in the classical limit and in the quantum SL and their expressions in terms of spin observables are given.

arXiv comment20 pages, 6 figures, 4 tables

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• Classification of time-reversal-invariant crystals with gauge structures
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• Topological Nematic Spin Liquid on the Square-Kagome Lattice
• Quantum phases in the frustrated Heisenberg model on the bilayer honeycomb lattice
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice
• Schwinger boson mean field study of the $J_1$-$J_2$ Heisenberg quantum antiferromagnet on the triangular lattice
• Emergent quasi-one-dimensionality in a kagomé magnet: A simple route to complexity
• Spin structure factors of chiral quantum spin liquids on the kagome lattice
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• Floquet engineering correlated materials with unpolarized light
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• Quantum phase diagram of a frustrated antiferromagnet on the bilayer honeycomb lattice
• Possible chiral spin liquid state in the $S=1/2$ kagome Heisenberg model
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• Candidate quantum spin liquids on the maple-leaf lattice
• Schwinger boson study of superconductivity mediated by antiferromagnetic spin-fluctuations
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• Quantum spin liquid and magnetic order in a two-dimensional non-symmorphic lattice: considering the distorted Kagome lattice of Volborthite
• Classical phase diagram of the stuffed honeycomb lattice
• Why the Schwinger Boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model
• Nematic quantum phases in the bilayer honeycomb antiferromagnet
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Schwinger boson mean field perspective on emergent spins in diluted Heisenberg antiferromagnets
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Schwinger boson study of the $J_1$-$J_2$-$J_3$ kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• Broken discrete and continuous symmetries in two dimensional spiral antiferromagnets
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Classical and quantum spin liquids
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
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• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature