  We develop a systematic variational coherent state expansion for the
many-body ground state of the spin-boson model, in which a quantum two-level
system is coupled to a continuum of harmonic oscillators. Energetic constraints
at the heart of this technique are rationalized in terms of polarons
(displacements of the bath states in agreement with classical expectations) and
antipolarons (counter-displacements due to quantum tunneling effects). We
present a comprehensive study of the ground state two-level system population
and coherence as a function of tunneling amplitude, dissipation strength, and
bias (akin to asymmetry of the double well potential defining the two-state
system). The entanglement among the different environmental modes is
investigated by looking at spectroscopic signatures of the bipartite
entanglement entropy between a given environmental mode and all the other
modes. We observe a drastic change in behavior of this entropy for increasing
dissipation, indicative of the entangled nature of the environmental states. In
addition, the entropy spreads over a large energy range at strong dissipation,
a testimony to the wide entanglement window characterizing the underlying Kondo
state. Finally, comparisons to accurate numerical renormalization group
calculations and to the exact Bethe Ansatz solution of the model demonstrate
the rapid convergence of our variationally-optimized multi-polaron expansion,
suggesting that it should also be a useful tool for dissipative models of
greater complexity, as relevant for numerous systems of interest in quantum
physics and chemistry.
