Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-order quantum phase transitions as condensations in the space of
  states   We demonstrate that a large class of first-order quantum phase transitions,
namely, transitions in which the ground state energy per particle is continuous
but its first order derivative has a jump discontinuity, can be described as a
condensation in the space of states. Given a system having Hamiltonian
$H=K+gV$, where $K$ and $V$ are two non commuting operators acting on the space
of states $\mathbb{F}$, we may always write
$\mathbb{F}=\mathbb{F}_\mathrm{cond} \oplus \mathbb{F}_\mathrm{norm}$ where
$\mathbb{F}_\mathrm{cond}$ is the subspace spanned by the eigenstates of $V$
with minimal eigenvalue and
$\mathbb{F}_\mathrm{norm}=\mathbb{F}_\mathrm{cond}^\perp$. If, in the
thermodynamic limit, $M_\mathrm{cond}/M \to 0$, where $M$ and $M_\mathrm{cond}$
are, respectively, the dimensions of $\mathbb{F}$ and
$\mathbb{F}_\mathrm{cond}$, the above decomposition of $\mathbb{F}$ becomes
effective, in the sense that the ground state energy per particle of the
system, $\epsilon$, coincides with the smaller between $\epsilon_\mathrm{cond}$
and $\epsilon_\mathrm{norm}$, the ground state energies per particle of the
system restricted to the subspaces $\mathbb{F}_\mathrm{cond}$ and
$\mathbb{F}_\mathrm{norm}$, respectively:
$\epsilon=\min\{\epsilon_\mathrm{cond},\epsilon_\mathrm{norm}\}$. It may then
happen that, as a function of the parameter $g$, the energies
$\epsilon_\mathrm{cond}$ and $\epsilon_\mathrm{norm}$ cross at
$g=g_\mathrm{c}$. In this case, a first-order quantum phase transition takes
place between a condensed phase (system restricted to the small subspace
$\mathbb{F}_\mathrm{cond}$) and a normal phase (system spread over the large
subspace $\mathbb{F}_\mathrm{norm}$)....

26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: econ
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc