We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin chains (exchange $J$ ) that are weakly coupled via intermediate ``dangling'' spins (exchange ${J}^{\ensuremath{'}}$). Using one-dimensional bosonization, renormalization-group methods, and current algebra techniques, the ground state is determined in the limit ${J}^{\ensuremath{'}}⪡J$. We find that the dangling spins and chain spins form a spiral with $O(1)$ and $O({J}^{\ensuremath{'}}/J)$ static moments, respectively, atop of which the chain spins exhibit a smaller $O[{({J}^{\ensuremath{'}}/J)}^{2}]$ antiferromagnetically ordered component along the axis perpendicular to the spiral plane.We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin chains (exchange $J$) that are weakly coupled via intermediate ``dangling'' spins (exchange ${J}^{\ensuremath{'}}$). Using one-dimensional bosonization, renormalization-group methods, and current algebra techniques, the ground state is determined in the limit ${J}^{\ensuremath{'}}⪡J$. We find that the dangling spins and chain spins form a spiral with $O(1)$ and $O({J}^{\ensuremath{'}}/J)$ static moments, respectively, atop of which the chain spins exhibit a smaller $O[{({J}^{\ensuremath{'}}/J)}^{2}]$ antiferromagnetically ordered component along the axis perpendicular to the spiral plane.

arXiv:0807.0285Physical Review BNov 18, 200851 citations

Ordered phases of the anisotropic kagome-lattice antiferromagnet in a magnetic field

Edwin Miles Stoudenmire, Leon Balents

The antiferromagnetic Heisenberg model on an anisotropic kagome lattice may be a good minimal model for real magnetic systems as well as a limit from which the isotropic case can be better understood. We therefore study the nearest-neighbor Heisenberg antiferromagnet on an anisotropic kagome lattice in a magnetic field. Such a system should be well described by weakly interacting spin chains, and we motivate a general form for the interaction by symmetry considerations and by perturbatively projecting out the interchain spins. In the spin- $1∕2$ case, we find that the system exhibits a quantum phase transition from a ferrimagnetic ordered state to an $XY$ ordered state as the field is increased. Finally, we discuss the appearance of magnetization plateaux in the ferrimagnetic phase.The antiferromagnetic Heisenberg model on an anisotropic kagome lattice may be a good minimal model for real magnetic systems as well as a limit from which the isotropic case can be better understood. We therefore study the nearest-neighbor Heisenberg antiferromagnet on an anisotropic kagome lattice in a magnetic field. Such a system should be well described by weakly interacting spin chains, and we motivate a general form for the interaction by symmetry considerations and by perturbatively projecting out the interchain spins. In the spin-$1∕2$ case, we find that the system exhibits a quantum phase transition from a ferrimagnetic ordered state to an $XY$ ordered state as the field is increased. Finally, we discuss the appearance of magnetization plateaux in the ferrimagnetic phase.

arXiv:0712.2269Physical Review BMay 8, 200815 citations

Spin- 12 Heisenberg antiferromagnet on an anisotropic kagome lattice

P. H. Y. Li, R. F. Bishop, C. E. Campbell +3 more

We use the coupled-cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin- $\frac{1}{2}$ moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants ${J}_{1}>0$ along two of the three lattice directions and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$ along the third. In the classical limit, the ground-state (GS) phase for $\ensuremath{\kappa}<\frac{1}{2}$ has collinear ferrimagnetic (N\'eel${}^{\ensuremath{'}}$) order where the ${J}_{2}$ -coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $\ensuremath{\kappa}>\frac{1}{2}$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin- $\frac{1}{2}$ case, we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $\ensuremath{\kappa}$, namely, for $0<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}$ for the N\'eel${}^{\ensuremath{'}}$ state and for (at least part of) the region $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$, which includes the isotropic kagome point $\ensuremath{\kappa}=1$ where the stable GS phase is now believed to be a topological ( ${\mathbb{Z}}_{2}$ ) spin liquid. Our best numerical estimates are ${\ensuremath{\kappa}}_{{c}_{1}}=0.515\ifmmode\pm\else\textpm\fi{}0.015$ and ${\ensuremath{\kappa}}_{{c}_{2}}=1.82\ifmmode\pm\else\textpm\fi{}0.03$.We use the coupled-cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-$\frac{1}{2}$ moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants ${J}_{1}>0$ along two of the three lattice directions and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$ along the third. In the classical limit, the ground-state (GS) phase for $\ensuremath{\kappa}<\frac{1}{2}$ has collinear ferrimagnetic (N\'eel${}^{\ensuremath{'}}$) order where the ${J}_{2}$-coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $\ensuremath{\kappa}>\frac{1}{2}$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin-$\frac{1}{2}$ case, we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $\ensuremath{\kappa}$, namely, for $0<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}$ for the N\'eel${}^{\ensuremath{'}}$ state and for (at least part of) the region $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$, which includes the isotropic kagome point $\ensuremath{\kappa}=1$ where the stable GS phase is now believed to be a topological (${\mathbb{Z}}_{2}$) spin liquid. Our best numerical estimates are ${\ensuremath{\kappa}}_{{c}_{1}}=0.515\ifmmode\pm\else\textpm\fi{}0.015$ and ${\ensuremath{\kappa}}_{{c}_{2}}=1.82\ifmmode\pm\else\textpm\fi{}0.03$.

arXiv:1208.3989Physical Review BDec 4, 201229 citations

We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin chains (exchange

J

) that are weakly coupled via intermediate ``dangling'' spins (exchange ${J}^{\ensuremath{'}}$). Using one-dimensional bosonization, renormalization-group methods, and current algebra techniques, the ground state is determined in the limit ${J}^{\ensuremath{'}}⪡J$. We find that the dangling spins and chain spins form a spiral with

O(1)

and $O({J}^{\ensuremath{'}}/J)$ static moments, respectively, atop of which the chain spins exhibit a smaller $O[{({J}^{\ensuremath{'}}/J)}^{2}]$ antiferromagnetically ordered component along the axis perpendicular to the spiral plane.

1∕2

case, we find that the system exhibits a quantum phase transition from a ferrimagnetic ordered state to an

XY

ordered state as the field is increased. Finally, we discuss the appearance of magnetization plateaux in the ferrimagnetic phase.

We use the coupled-cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-

\frac{1}{2}

moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants

{J}_{1}>0

along two of the three lattice directions and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$ along the third. In the classical limit, the ground-state (GS) phase for $\ensuremath{\kappa}<\frac{1}{2}$ has collinear ferrimagnetic (N\'eel${}^{\ensuremath{'}}$) order where the

{J}_{2}

-coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $\ensuremath{\kappa}>\frac{1}{2}$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin-

\frac{1}{2}

case, we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $\ensuremath{\kappa}$, namely, for $0<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}$ for the N\'eel${}^{\ensuremath{'}}$ state and for (at least part of) the region $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$, which includes the isotropic kagome point $\ensuremath{\kappa}=1$ where the stable GS phase is now believed to be a topological (

{\mathbb{Z}}_{2}

) spin liquid. Our best numerical estimates are ${\ensuremath{\kappa}}_{{c}_{1}}=0.515\ifmmode\pm\else\textpm\fi{}0.015$ and ${\ensuremath{\kappa}}_{{c}_{2}}=1.82\ifmmode\pm\else\textpm\fi{}0.03$.