solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看15172次
Analytical results on the Heisenberg spin chain in a magnetic field. (arXiv:1901.05878v1 [cond-mat.stat-mech])
来源于:arXiv
We obtain the ground state magnetization of the Heisenberg and XXZ spin
chains in a magnetic field $h$ as a series in $\sqrt{h_c-h}$, where $h_c$ is
the smallest field for which the ground state is fully polarized. All the
coefficients of the series can be computed in closed form through a recurrence
formula that involves only algebraic manipulations. The radius of convergence
of the series in the full range $0<h\leq h_c$ is studied numerically.
To that end we express the free energy at mean magnetization per site
$-1/2\leq \langle \sigma^z_i\rangle\leq 1/2$ as a series in $1/2-\langle
\sigma^z_i\rangle$ whose coefficients can be similarly recursively computed in
closed form. This series converges for all $0\leq \langle \sigma^z_i\rangle\leq
1/2$. The recurrence is nothing but the Bethe equations when their roots are
written as a double series in their corresponding Bethe number and in
$1/2-\langle \sigma^z_i\rangle$. It can also be used to derive the corrections
in finite size, tha 查看全文>>