Equilibrium dynamics of the sub-ohmic spin-boson model at finite temperature

We use the full-density matrix numerical renormalization group method to calculate the equilibrium dynamical correlation function C(ω) of the spin operator σ_z at finite temperature for the sub-ohmic spin-boson model. A peak is observed at the frequency ω_T∼ T in the curve of C(ω). The curve merges with the zero-temperature C(ω) in \omega \gg \omega_\rm T and deviates significantly from the zero-temperature curve in ω «ω _T.