Ising-chain Nambu spinor
= Ising-chain Nambu spinor
{c}
{title2=$\Psi_k=(c_k,-ic_{-k}^\dagger)^T$}
With Fourier convention $c_n=N^{-1/2}\sum_ke^{-ikn}c_k$, the <Transverse-field Ising model> has $H=J\sum_k\Psi_k^\dagger[(g-\cos k)\sigma_z-\sin k\,\sigma_x]\Psi_k$. Expanding the spinor retains the constant $-JgN$ and pairs $k$ with $-k$. The physical <quasiparticle> energy is twice the positive matrix <eigenvalue> times $J$, because both <momentum> partners occur in the Nambu sum.