We present a numerical diagonalization study of two one-dimensional $S=\frac{1}{2}$ antiferromagnetic Heisenberg chains, having nearest-neighbor and Haldane-Shastry ( $\frac{1}{{r}^{2}}$ ) interactions, respectively. We have obtained the $T=0$ dynamical correlation function, ${S}^{\ensuremath{\alpha}\ensuremath{\alpha}}(q, \ensuremath{\omega})$, for chains of length $N=8\ensuremath{-}28$. We have studied ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ for the Heisenberg chain in zero field, and from finite-size scaling we have obtained a limiting behavior that for large $\ensuremath{\omega}$ deviates from the conjecture proposed earlier by M\"uller et al. For both chains we describe the behavior of ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ and ${S}^{\mathrm{xx}}(q, \ensuremath{\omega})$ for selected values of the applied field, and compare with previous work by M\"uller et al. and Talstra and Haldane. Suggestions for future finite-field neutron scattering experiments are made.We present a numerical diagonalization study of two one-dimensional $S=\frac{1}{2}$ antiferromagnetic Heisenberg chains, having nearest-neighbor and Haldane-Shastry ($\frac{1}{{r}^{2}}$) interactions, respectively. We have obtained the $T=0$ dynamical correlation function, ${S}^{\ensuremath{\alpha}\ensuremath{\alpha}}(q, \ensuremath{\omega})$, for chains of length $N=8\ensuremath{-}28$. We have studied ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ for the Heisenberg chain in zero field, and from finite-size scaling we have obtained a limiting behavior that for large $\ensuremath{\omega}$ deviates from the conjecture proposed earlier by M\"uller et al. For both chains we describe the behavior of ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ and ${S}^{\mathrm{xx}}(q, \ensuremath{\omega})$ for selected values of the applied field, and compare with previous work by M\"uller et al. and Talstra and Haldane. Suggestions for future finite-field neutron scattering experiments are made.

Physical review. B, Condensed matterSep 1, 199618 citations

Quasi-classical approximation in neutron scattering

George Kosaly, Roy E. Turner

Physics LettersOct 1, 19621 citation

Some Results from Scattering Theory

Khosrow Chadan, Pierre C. Sabatier

Springer eBooksJan 1, 19771 citation

Experimental evidence for the Haldane gap in a spin-1 nearly isotropic, antiferromagnetic chain

W. J. L. Buyers, Rose M. Morra, Robin L. Armstrong +3 more

Neutron scattering has shown that the lowest spin excitations in the spin-1 antiferromagnet ${\mathrm{CsNiCl}}_{3}$ in its one-dimensional phase occur at finite frequency. After allowance for the known weak interchain coupling the gap is found to be in good agreement with recent numerical calculations. The results support the Haldane conjecture that in integral-spin chains with isotropic interactions a gap separates the ground state from the excitations.Neutron scattering has shown that the lowest spin excitations in the spin-1 antiferromagnet ${\mathrm{CsNiCl}}_{3}$ in its one-dimensional phase occur at finite frequency. After allowance for the known weak interchain coupling the gap is found to be in good agreement with recent numerical calculations. The results support the Haldane conjecture that in integral-spin chains with isotropic interactions a gap separates the ground state from the excitations.

Physical Review LettersJan 27, 1986433 citations

Potential Scattering Theory

WORLD SCIENTIFIC eBooksAug 1, 20090 citations

We present a numerical diagonalization study of two one-dimensional

S=\frac{1}{2}

antiferromagnetic Heisenberg chains, having nearest-neighbor and Haldane-Shastry (

\frac{1}{{r}^{2}}

) interactions, respectively. We have obtained the

T=0

dynamical correlation function, ${S}^{\ensuremath{\alpha}\ensuremath{\alpha}}(q, \ensuremath{\omega})$, for chains of length $N=8\ensuremath{-}28$. We have studied ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ for the Heisenberg chain in zero field, and from finite-size scaling we have obtained a limiting behavior that for large $\ensuremath{\omega}$ deviates from the conjecture proposed earlier by M\"uller et al. For both chains we describe the behavior of ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ and ${S}^{\mathrm{xx}}(q, \ensuremath{\omega})$ for selected values of the applied field, and compare with previous work by M\"uller et al. and Talstra and Haldane. Suggestions for future finite-field neutron scattering experiments are made.

Neutron scattering has shown that the lowest spin excitations in the spin-1 antiferromagnet

{\mathrm{CsNiCl}}_{3}

in its one-dimensional phase occur at finite frequency. After allowance for the known weak interchain coupling the gap is found to be in good agreement with recent numerical calculations. The results support the Haldane conjecture that in integral-spin chains with isotropic interactions a gap separates the ground state from the excitations.