First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagom\'e lattice

We believe that a necessary first step in understanding the ground state properties of the spin-${\scriptstyle\frac{1}{2}}$ kagome Heisenberg antiferromagnet is a better understanding of this model's very large number of low energy singlet states. A description of the low energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular when these turn on the delicate balan...

The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-1D strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charg...

We use the coupled cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-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 $J_{2} \equiv \kappa J_{1} > 0$ along the third. In the classical limit the ground-state (GS) phase for...

The $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet, which for instance is related to the experimentally accessible spinel oxide Na$_4$Ir$_3$O$_8$, allows to study the interplay of geometrical frustration and quantum as well as thermal fluctuations in three dimensions. We use 16 terms of a high-temperature series expansion complemented by the entropy-method interpolation to examine the specific heat and the uniform susceptibility of the $S=1/2$ hyperkagome-lattice Heis...

We propose in this work an effective field theory description of the chiral spin liquid state in Heisenberg spin system on kagom\'e lattice.To this end, we derive the low-energy effective theory of kagom\'e (isotropic) Heisenberg antiferromagnet around its ordered ground states found numerically and show that quantum fluctuations induced by further neighbor spin exchanges are equally strong as those from first neighbor.We use a chiral order parameter theory to argue for the o...

We use a second-order rotational invariant Green's function method (RGM) and the high-temperature expansion (HTE) to calculate the thermodynamic properties, of the kagome-lattice spin-$S$ Heisenberg antiferromagnet with nearest-neighbor exchange $J$. While the HTE yields accurate results down to temperatures of about $T/S(S+1) \sim J$, the RGM provides data for arbitrary $T \ge 0$. For the ground state we use the RGM data to analyze the $S$-dependence of the excitation spectr...

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenari...

Dynamics of classical Heisenberg spins, ${\bf S}_i=({\bf s}_i,S_{iz})$, on the Kagom\'{e} lattice has been studied. An ideal Heisenberg Kagom\'{e} antiferromagnet is known to remain disordered down to T=0 due to the macroscopic degeneracy of the ground state. Through the study, however, we find that ${\bf S}_i$ and their planar components ${\bf s}_i$ behave in a qualitatively different way and especially planar spins (${\bf s}_i$) show the exotic glass-like transition in the ...

Motivated by recent density-matrix renormalization group (DMRG) calculations [Yan, Huse, and White, Science 332, 1173 (2011)], which claimed that the ground state of the nearest-neighbor spin-1/2 Heisenberg antiferromagnet on the kagome lattice geometry is a fully gapped spin liquid with numerical signatures of Z2 gauge structure, and a further theoretical work [Lu, Ran, and Lee, Phys. Rev. B 83, 224413 (2011)], which gave a classification of all Schwinger-fermion mean-field ...

We have studied the Heisenberg antiferromagnets on two-dimensional frustrated lattices, triangular and kagome lattices using linear spin-wave theory. A collinear ground state ordering is possible if one of the three bonds in each triangular plaquette of the lattice becomes weaker or frustrated. We study spiral order in the Heisenberg model along with Dzyaloshinskii-Moriya (DM) interaction and in the presence of a magnetic field. The quantum corrections to the ground state ene...