Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Return probability after a quench from a domain wall initial state in
  the spin-1/2 XXZ chain   We study the return probability and its imaginary ($\tau$) time continuation
after a quench from a domain wall initial state in the XXZ spin chain, focusing
mainly on the region with anisotropy $|\Delta|< 1$. We establish exact Fredholm
determinant formulas for those, by exploiting a connection to the six vertex
model with domain wall boundary conditions. In imaginary time, we find the
expected scaling for a partition function of a statistical mechanical model of
area proportional to $\tau^2$, which reflects the fact that the model exhibits
the limit shape phenomenon. In real time, we observe that in the region
$|\Delta|<1$ the decay for large times $t$ is nowhere continuous as a function
of anisotropy: it is either gaussian at root of unity or exponential otherwise.
As an aside, we also determine that the front moves as $x_{\rm
f}(t)=t\sqrt{1-\Delta^2}$, by analytic continuation of known arctic curves in
the six vertex model. Exactly at $|\Delta|=1$, we find the return probability
decays as $e^{-\zeta(3/2) \sqrt{t/\pi}}t^{1/2}O(1)$. It is argued that this
result provides an upper bound on spin transport. In particular, it suggests
that transport should be diffusive at the isotropic point for this quench.

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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
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The categories of this paper are: cs
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th