Physical review. B, Condensed matter

Edge states in Schwinger-boson mean-field theory of low-dimensional quantum antiferromagnets

Tai Kai Ng

Published May 1, 1993• 10 citations

Abstract

The origin and properties of the S=1/2 end states in S=1 open spin chains is explained within the framework of Schwinger-boson mean-field theory. Moreover, we show that in two dimensions (square lattice), corresponding edge states exist with structures depending on spin magnitude S.

DOI: 10.1103/physrevb.47.11575

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Physical review. B, Condensed matter

Edge states in Schwinger-boson mean-field theory of low-dimensional quantum antiferromagnets

Tai Kai Ng

Published May 1, 1993• 10 citations

Publisher

Abstract

DOI: 10.1103/physrevb.47.11575

Related papers

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Physical review. B, Condensed matterApr 1, 199224 citations

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Congjun Wu, Bin Chen, Xi Dai +2 more

The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at $T=0 \mathrm{K}.$ These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at $T>0 \mathrm{K},$ are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at $T=0 \mathrm{K}.$ These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at $T>0 \mathrm{K},$ are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.

arXiv:cond-mat/9904291Physical review. B, Condensed matterJul 1, 199965 citations

{m}^{\mathrm{MF}=0.306}

, to be in excellent agreement with published Monte Carlo results.

U(1)

gauge modes in the nonmagnetic phase. In the

{\mathbb{Z}}_{2}

liquid phase of the triangular lattice, we identify the topological degeneracy as well as vison states.

m_{s}=0.07566

, and the recent quantum Monte Carlo simulations on rather large lattice sizes have provided strong evidence to support these mean field results.

{\mathit{S}}_{\mathrm{edge}}

=S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a

{\mathit{S}}_{\mathrm{edge}}

=1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.

T=0 \mathrm{K}.

These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at

T>0 \mathrm{K},

are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.