Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition in complex-time Loschmidt echo of short and long range
  spin chain   We explain and exploit the random matrix formulation of the Loschmidt echo
for the XX spin chain, valid for multiple domain wall initial states and also
for a XX spin chain generalized with additional interactions to more
neighbours. For models with interactions decaying as $e^{-\alpha \left\vert
l-j\right\vert }/\left\vert l-j\right\vert ^{p+1}$, with $p$ integer or natural
number and $\alpha \geq 0$, we show that there are third order phase
transitions in a double scaling limit of the complex-time Loschmidt echo
amplitudes. For the long-range version of the chain, we use an exact result for
Toeplitz determinants with a pure Fisher-Hartwig singularity, to obtain exactly
the Loschmidt echo for complex times and discuss the associated Stokes
phenomena. We also study the case of a finite chain for one of the generalized
XX models.

34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ