  We investigate the thermodynamics and transient dynamics of the (unbiased)
Ohmic two-state system by exploiting the equivalence of this model to the
interacting resonant level model. For the thermodynamics, we show, by using the
numerical renormalization group (NRG) method, how the universal specific heat
and susceptibility curves evolve with increasing dissipation strength,
$\alpha$, from those of an isolated two-level system at vanishingly small
dissipation strength, with the characteristic activated-like behavior in this
limit, to those of the isotropic Kondo model in the limit $\alpha\to 1^{-}$.
For the transient dynamics of the two-level system, $P(t)=\langle
\sigma_{z}(t)\rangle$, with initial-state preparation $P(t\leq0)=+1$, we apply
the time-dependent extension of the NRG (TDNRG) to the interacting resonant
level model, and compare the results obtained with those from the
noninteracting-blip approximation (NIBA), the functional renormalization group
(FRG), and the time-dependent density matrix renormalization group (TD-DMRG).
We demonstrate excellent agreement on short to intermediate time scales between
TDNRG and TD-DMRG for $0\lesssim\alpha \lesssim 0.9$ for $P(t)$, and between
TDNRG and FRG in the vicinity of $\alpha=1/2$. Furthermore, we quantify the
error in the NIBA for a range of $\alpha$, finding significant errors in the
latter even for $0.1\leq \alpha\leq 0.4$. We also briefly discuss why the
long-time errors in the present formulation of the TDNRG prevents an
investigation of the crossover between coherent and incoherent dynamics. Our
results for $P(t)$ at short to intermediate times could act as useful
benchmarks for the development of new techniques to simulate the transient
dynamics of spin-boson problems.
