Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum phase transitions in the spin-boson model without the
  counterrotating terms   We study the spin-boson model without the counterrotating terms by a
numerically exact method based on variational matrix product states.
Surprisingly, the second-order quantum phase transition (QPT) is observed for
the sub-Ohmic bath in the rotating-wave approximations. Moreover, first-order
QPTs can also appear before the critical points. With the decrease of the bath
exponents, these first-order QPTs disappear successively, while the
second-order QPT remains robust. The second-order QPT is further confirmed by
multi-coherent-states variational studies, while the first-order QPT is
corroborated with the exact diagonalization in the truncated Hilbert space.
Extension to the Ohmic bath is also performed, and many first-order QPTs appear
successively in a wide coupling regime, in contrast to previous findings. The
previous pictures for many physical phenomena for the spin-boson model in the
rotating-wave approximation have to be modified at least at the strong
coupling.

14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga