= Ising-chain ground-state energy
{c}
{title2=$E_0=-\tfrac12\sum_k\epsilon_k$}
The vacuum of the diagonal <Bogoliubov quasiparticles> has the displayed energy. In the thermodynamic bulk, $E_0/N=-J(2\pi)^{-1}\int_{-\pi}^{\pi}\sqrt{1+g^2-2g\cos k}\,dk$. The <Hellmann–Feynman theorem> then gives the field <magnetization> $\sum_n\langle S_n^z\rangle=\sum_kJ(g-\cos k)/\epsilon_k$. Sector-dependent finite-chain boundary terms must be restored when exact finite-size levels are needed.
Back to article page
