Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entanglement between a qubit and the environment in the spin-boson model   The quantitative description of the quantum entanglement between a qubit and
its environment is considered. Specifically, for the ground state of the
spin-boson model, the entropy of entanglement of the spin is calculated as a
function of $\alpha$, the strength of the ohmic coupling to the environment,
and $\epsilon$, the level asymmetry. This is done by a numerical
renormalization group treatment of the related anisotropic Kondo model. For
$\epsilon=0$, the entanglement increases monotonically with $\alpha$, until it
becomes maximal for $\alpha \lim 1^-$. For fixed $\epsilon>0$, the entanglement
is a maximum as a function of $\alpha$ for a value, $\alpha = \alpha_M < 1$.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
2
The categories of this paper are: math