Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of excited-state quantum phase transitions for arbitrary
  number of degrees of freedom   Classical stationary points of an analytic Hamiltonian induce singularities
of the density of quantum energy levels and their flow with a control parameter
in the system's infinite-size limit. We show that for a system with $f$ degrees
of freedom, a non-degenerate stationary point with index $r$ causes a
discontinuity (for $r$ even) or divergence ($r$ odd) of the $(f-1)$ th
derivative of both density and flow of the spectrum. An increase of flatness
for a degenerate stationary point shifts the singularity to lower derivatives.
The findings are verified in an $f=3$ toy model.

35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs