This paper presents an overview of the properties of magnetic insulators, with emphasis on quantum effects. In particular, the consequences of strong quantum fluctuations on the low-energy properties of a number of systems are reviewed: the occurrence of a spin gap in spin-1 chains and other low-dimensional magnets; the presence of low-lying singlet excitations in several frustrated magnets; the interplay of orbital and spin fluctuations in orbitally degenerate Mott insulators. This review is intended as a pedagogical introduction to the field, and the formalism has been kept at a minimal level.This paper presents an overview of the properties of magnetic insulators, with emphasis on quantum effects. In particular, the consequences of strong quantum fluctuations on the low-energy properties of a number of systems are reviewed: the occurrence of a spin gap in spin-1 chains and other low-dimensional magnets; the presence of low-lying singlet excitations in several frustrated magnets; the interplay of orbital and spin fluctuations in orbitally degenerate Mott insulators. This review is intended as a pedagogical introduction to the field, and the formalism has been kept at a minimal level.

European Journal of PhysicsNov 1, 2000102 citations

Non-Kitaev spin liquids in Kitaev materials

Yaodong Li, Xu Yang, Yi Zhou +1 more

We point out that the Kitaev materials may not necessarily support Kitaev spin liquid. It is well known that having a Kitaev term in the spin interaction is not the sufficient condition for the Kitaev spin-liquid ground state. Many other spin liquids may be stabilized by the competing spin interactions of the systems. We thus explore the possibilities of non-Kitaev spin liquids in the honeycomb Kitaev materials. We carry out a systematic classification of gapped ${\mathbb{Z}}_{2}$ spin liquids using the Schwinger boson representation for the spin variables. The presence of strong spin-orbit coupling in the Kitaev materials brings new ingredients into the projective symmetry group classification of the non-Kitaev spin liquid. We predict the spectroscopic properties of these gapped non-Kitaev spin liquids. Moreover, among the gapped spin liquids that we discover, we identify the spin liquid whose spinon condensation leads to the zigzag magnetic order that was observed in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We further discuss the possibility of gapped ${\mathbb{Z}}_{2}$ spin liquid and the deconfined quantum criticality from the zigzag magnetic order to spin dimerization in pressurized $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.We point out that the Kitaev materials may not necessarily support Kitaev spin liquid. It is well known that having a Kitaev term in the spin interaction is not the sufficient condition for the Kitaev spin-liquid ground state. Many other spin liquids may be stabilized by the competing spin interactions of the systems. We thus explore the possibilities of non-Kitaev spin liquids in the honeycomb Kitaev materials. We carry out a systematic classification of gapped ${\mathbb{Z}}_{2}$ spin liquids using the Schwinger boson representation for the spin variables. The presence of strong spin-orbit coupling in the Kitaev materials brings new ingredients into the projective symmetry group classification of the non-Kitaev spin liquid. We predict the spectroscopic properties of these gapped non-Kitaev spin liquids. Moreover, among the gapped spin liquids that we discover, we identify the spin liquid whose spinon condensation leads to the zigzag magnetic order that was observed in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We further discuss the possibility of gapped ${\mathbb{Z}}_{2}$ spin liquid and the deconfined quantum criticality from the zigzag magnetic order to spin dimerization in pressurized $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.

arXiv:1903.00895Physical review. B./Physical review. BMay 13, 201915 citations

Classification of symmetry fractionalization in gapped Z2 spin liquids

Yang Qi, Meng Cheng

In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin- $\frac{1}{2}$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped ${\mathbb{Z}}_{2}$ spin liquids.In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$\frac{1}{2}$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped ${\mathbb{Z}}_{2}$ spin liquids.

arXiv:1606.04544Physical review. B./Physical review. BMar 19, 201823 citations

{\mathbb{Z}}_{2}

spin liquids using the Schwinger boson representation for the spin variables. The presence of strong spin-orbit coupling in the Kitaev materials brings new ingredients into the projective symmetry group classification of the non-Kitaev spin liquid. We predict the spectroscopic properties of these gapped non-Kitaev spin liquids. Moreover, among the gapped spin liquids that we discover, we identify the spin liquid whose spinon condensation leads to the zigzag magnetic order that was observed in

{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}

and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We further discuss the possibility of gapped

{\mathbb{Z}}_{2}

spin liquid and the deconfined quantum criticality from the zigzag magnetic order to spin dimerization in pressurized $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.

\frac{1}{2}

per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped

{\mathbb{Z}}_{2}

spin liquids.