<i>S</i>=1 antiferromagnetic Heisenberg chain in a magnetic field

Abstract

A one-dimensional S=1 Heisenberg antiferromagnet in a magnetic field H (\ensuremath{\parallel}z axis) at T=0 is studied by numerical diagonalizations up to N=16. We give the magnetization curve at the thermodynamic limit, and derive an anomaly at ${\mathit{H}}_{\mathit{c}1}$ (=\ensuremath{\Delta}), where \ensuremath{\Delta} is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈${\mathit{S}}_{0}^{\mathit{x}}$${\mathit{S}}_{\mathit{r}}^{\mathit{x}}$〉\ensuremath{\sim}(-1${)}^{\mathit{r}}$${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, and the transverse staggered susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$ (=4). The exponent \ensuremath{\eta} has a minimum (\ensuremath{\eta}\ensuremath{\simeq}0.3) at magnetization m\ensuremath{\simeq}1/3 and \ensuremath{\eta}\ensuremath{\simeq}0.5 at ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$. If the system is quasi-one-dimensional, even small interchain couplings can create a canted N\'eel order, within a mean-field approximation for interchain interactions. This is consistent with a recent NMR measurement for Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$(${\mathrm{ClO}}_{4}$) (NENP) at low temperature.