We study the quantum-spin-liquid phase in a variant of the Kitaev model where the bonds of the honeycomb lattice are distributed in a Kekul\'e pattern. The system supports gapped and gapless ${Z}_{2}$ quantum spin liquids with interesting differences from the original Kitaev model, the most notable being a gapped ${Z}_{2}$ spin liquid on a kagome lattice. Perturbing the exactly solvable model with antiferromagnetic Heisenberg perturbations, we find a magnetically ordered phase stabilized by a quantum ``order by disorder'' mechanism, as well as an exotic continuous quantum phase transition between the topological spin liquid and this magnetically ordered phase. Using a combination of field theory and Monte Carlo simulations, we find that the transition likely belongs to the $3D\text{\ensuremath{-}}XY\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ universality class.We study the quantum-spin-liquid phase in a variant of the Kitaev model where the bonds of the honeycomb lattice are distributed in a Kekul\'e pattern. The system supports gapped and gapless ${Z}_{2}$ quantum spin liquids with interesting differences from the original Kitaev model, the most notable being a gapped ${Z}_{2}$ spin liquid on a kagome lattice. Perturbing the exactly solvable model with antiferromagnetic Heisenberg perturbations, we find a magnetically ordered phase stabilized by a quantum ``order by disorder'' mechanism, as well as an exotic continuous quantum phase transition between the topological spin liquid and this magnetically ordered phase. Using a combination of field theory and Monte Carlo simulations, we find that the transition likely belongs to the $3D\text{\ensuremath{-}}XY\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ universality class.

arXiv:1501.07582Physical Review BApr 16, 201513 citations

The Dynamical Topological Phase Transitions in a Quenched Kitaev Model

Li-Na Luan, Shuai Liu, Zhi-Xu Zhang

Jan 1, 20260 citations

Quantum Spin Liquids in Kitaev and Kagome Systems

Robert Schaffer

Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the source of much recent theoretical and experimental interest. These systems are characterised by their long ranged entangled states, preserve symmetries down to zero Kelvin, and have been shown to exhibit fascinating properties such as a topological ground state degeneracy and fractionalised spin excitations. In this thesis, we study several of these phases. The first, Kitaev spin liquids, appear in strongly spin-orbit coupled systems, where the SU(2) spin symmetry is broken. Within our mean field approach, we study the quantum phase transition from the gapless Z 2 spin liquid to a magnetically ordered phase within the Heisenberg-Kitaev model. Beyond the mean field theory, we argue that the gauge structure of the spin liquid plays a crucial role in this transition, leading to a confinement of spinons and the generation of magnetic order. We also discuss the three-dimensional iridate compounds, where the Kitaev spin liquid phase has topologically protected bulk and surface excitations. We next discuss spin liquids appearing on the geometrically frustrated kagome lattice. First, we consider non-Kramers spin liquids, in which the spin structure of the theory is protected by lattice, rather than time-reversal, symmetry. As a result, more phases are allowed, which have different properties than those which transform as Kramers doublets. In addition, these may have positive experimental signatures in the Raman scattering intensity, offering a clear path to detect such a state. Finally, we examine possible spin liquid phases on a breathing kagome lattice, where we find a stable Z2 spin liquid to be the ground state. This may help to guide future numerical studies of the kagome lattice Heisenberg model, and may also be relevant to DQVOF, a recently discovered spin liquid candidate compound.Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the source of much recent theoretical and experimental interest. These systems are characterised by their long ranged entangled states, preserve symmetries down to zero Kelvin, and have been shown to exhibit fascinating properties such as a topological ground state degeneracy and fractionalised spin excitations. In this thesis, we study several of these phases. The first, Kitaev spin liquids, appear in strongly spin-orbit coupled systems, where the SU(2) spin symmetry is broken. Within our mean field approach, we study the quantum phase transition from the gapless Z 2 spin liquid to a magnetically ordered phase within the Heisenberg-Kitaev model. Beyond the mean field theory, we argue that the gauge structure of the spin liquid plays a crucial role in this transition, leading to a confinement of spinons and the generation of magnetic order. We also discuss the three-dimensional iridate compounds, where the Kitaev spin liquid phase has topologically protected bulk and surface excitations. We next discuss spin liquids appearing on the geometrically frustrated kagome lattice. First, we consider non-Kramers spin liquids, in which the spin structure of the theory is protected by lattice, rather than time-reversal, symmetry. As a result, more phases are allowed, which have different properties than those which transform as Kramers doublets. In addition, these may have positive experimental signatures in the Raman scattering intensity, offering a clear path to detect such a state. Finally, we examine possible spin liquid phases on a breathing kagome lattice, where we find a stable Z2 spin liquid to be the ground state. This may help to guide future numerical studies of the kagome lattice Heisenberg model, and may also be relevant to DQVOF, a recently discovered spin liquid candidate compound.

Nov 1, 20160 citations

We study the quantum-spin-liquid phase in a variant of the Kitaev model where the bonds of the honeycomb lattice are distributed in a Kekul\'e pattern. The system supports gapped and gapless

{Z}_{2}

quantum spin liquids with interesting differences from the original Kitaev model, the most notable being a gapped

{Z}_{2}

spin liquid on a kagome lattice. Perturbing the exactly solvable model with antiferromagnetic Heisenberg perturbations, we find a magnetically ordered phase stabilized by a quantum ``order by disorder'' mechanism, as well as an exotic continuous quantum phase transition between the topological spin liquid and this magnetically ordered phase. Using a combination of field theory and Monte Carlo simulations, we find that the transition likely belongs to the $3D\text{\ensuremath{-}}XY\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ universality class.