S=1 antiferromagnetic Heisenberg chain in a magnetic field

A one-dimensional S=1 Heisenberg antiferromagnet in a magnetic field H (∥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 ${\mathit{H}}_{\mathit{c}1}$ (=Δ), where Δ is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈${\mathit{S}}_0^{\mathit{x}}$ ${\mathit{S}}_{\mathit{r}}^{\mathit{x}}$〉∼(-1${)}^{\mathit{r}}$ ${\mathit{r}}^{\mathrm{-}\mathrm{\eta }}$, and the transverse staggered susceptibility ${\mathrm{\chi }}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$ (=4). The exponent η has a minimum (η≃0.3) at magnetization m≃1/3 and η≃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 Néel 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.