Using the valence-bond-solid (VBS) approach and the Schwinger-boson mean-field approximation, we study the dependence of the Haldane gap of a spin-1 linear-chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter \ensuremath{\Delta} and the constraint factor \ensuremath{\lambda}. As a result, the Haldane gap is reduced by a factor \ensuremath{\sim} ${\mathit{n}}_{\mathit{i}}^{2/3}$ , with ${\mathit{n}}_{\mathit{i}}$ as the impurity concentration, and eventually collapses at ${\mathit{n}}_{\mathit{i}}$ \ensuremath{\sim}1/\ensuremath{\xi} with \ensuremath{\xi} as the VBS correlation length. This theoretical prediction can be verified by neutron-scattering experiments.Using the valence-bond-solid (VBS) approach and the Schwinger-boson mean-field approximation, we study the dependence of the Haldane gap of a spin-1 linear-chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter \ensuremath{\Delta} and the constraint factor \ensuremath{\lambda}. As a result, the Haldane gap is reduced by a factor \ensuremath{\sim}${\mathit{n}}_{\mathit{i}}^{2/3}$, with ${\mathit{n}}_{\mathit{i}}$ as the impurity concentration, and eventually collapses at ${\mathit{n}}_{\mathit{i}}$\ensuremath{\sim}1/\ensuremath{\xi} with \ensuremath{\xi} as the VBS correlation length. This theoretical prediction can be verified by neutron-scattering experiments.

arXiv:cond-mat/9301035Physical review. B, Condensed matterMay 1, 19932 citations

Non-Abelian bosonization and Haldane’s conjecture

D. C. Cabra, Pierre Pujol, Cecilia von Reichenbach

We study the long-wavelength limit of a spin $S$ Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level $2S$ $\mathrm{SU}(2)$ Wess-Zumino-Witten (WZW) model. This effective theory is then mapped into a compact $U(1)$ boson interacting with ${Z}_{2S}$ parafermions. The analysis of this effective theory allows us to show that when $S$ is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case and the ${\mathrm{SU}(2)}_{2S}$ WZW model flows towards the ${\mathrm{SU}(2)}_{1}$ stable fixed point. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin $S$ .We study the long-wavelength limit of a spin $S$ Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level $2S$ $\mathrm{SU}(2)$ Wess-Zumino-Witten (WZW) model. This effective theory is then mapped into a compact $U(1)$ boson interacting with ${Z}_{2S}$ parafermions. The analysis of this effective theory allows us to show that when $S$ is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case and the ${\mathrm{SU}(2)}_{2S}$ WZW model flows towards the ${\mathrm{SU}(2)}_{1}$ stable fixed point. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin $S$.

arXiv:hep-th/9802014Physical review. B, Condensed matterJul 1, 199824 citations

Haldane and Dimer Gap in General Double Spin-Chain Models

KIYOMI OKAMOTO

Jan 1, 19970 citations

Quantum Antiferromagnets in a Magnetic Field

Daniel Loss, Bruce Normand

Motivated by recent experiments on low-dimensional quantum magnets in applied magnetic fields, we present a theoretical analysis of their properties based on the nonlinear sigma model. The spin stiffness and a 1/N expansion are used to map the regimes of spin-gap behavior, predominantly linear magnetization, and spin saturation. A two-parameter renormalization-group study gives the characteristic properties over the entire parameter range. The model is relevant to many systems exhibiting Haldane physics, and is applied here to the two-chain spin ladder compound CuHpCl.Motivated by recent experiments on low-dimensional quantum magnets in applied magnetic fields, we present a theoretical analysis of their properties based on the nonlinear sigma model. The spin stiffness and a 1/N expansion are used to map the regimes of spin-gap behavior, predominantly linear magnetization, and spin saturation. A two-parameter renormalization-group study gives the characteristic properties over the entire parameter range. The model is relevant to many systems exhibiting Haldane physics, and is applied here to the two-chain spin ladder compound CuHpCl.

arXiv:cond-mat/9804151Acta Physica Polonica BApr 15, 19982 citations

{\mathit{n}}_{\mathit{i}}^{2/3}

, with

{\mathit{n}}_{\mathit{i}}

as the impurity concentration, and eventually collapses at

{\mathit{n}}_{\mathit{i}}

\ensuremath{\sim}1/\ensuremath{\xi} with \ensuremath{\xi} as the VBS correlation length. This theoretical prediction can be verified by neutron-scattering experiments.

We study the long-wavelength limit of a spin

S

Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level

2S

\mathrm{SU}(2)

Wess-Zumino-Witten (WZW) model. This effective theory is then mapped into a compact

U(1)

boson interacting with

{Z}_{2S}

parafermions. The analysis of this effective theory allows us to show that when

S

is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case and the

{\mathrm{SU}(2)}_{2S}

WZW model flows towards the

{\mathrm{SU}(2)}_{1}

stable fixed point. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin

S