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Ground state of the dissipative two-state system is investigated by means ofthe Lanczos diagonalization method. We adopted the Hilbert-space-reductionscheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelmingreservoir Hilbert space to being tractable in computers. Both theimplementation of the algorithm and the precision applied for the presentsystem are reported in detail. We evaluate the dynamical susceptibility(resolvent) with the continued-fraction-expansion formula. Through analysingthe resolvent over a frequency range, whose range is often called `interesting'frequency, we obtain the damping rate and the oscillation frequency. Ourresults agree with those of a recent quantum Monte-Carlo study, which concludesthat the critical dissipation from oscillatory to over-damped behaviordecreases as the tunneling amplitude is strengthened

Numerical analysis of the dissipative two-state system with the density-matrix Hilbert-space-reduction algorithm