Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fisher information approach to non-equilibrium phase transitions in
  quantum XXZ spin chain with boundary noise   We investigated quantum critical behaviours in the non-equilibrium steady
state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher
information. The latter represents the distance between two infinitesimally
close states, and its superextensive size scaling witnesses a critical
behaviour due to a phase transition, since all the interaction terms are
extensive. Perturbatively in the noise strength, we found superextensive Fisher
information at anisotropy $|\Delta|\leqslant1$ and irrational
$\frac{\arccos\Delta}{\pi}$ irrespective of the order of two non-commuting
limits, i.e. the thermodynamic limit and the limit of sending
$\frac{\arccos\Delta}{\pi}$ to an irrational number via a sequence of rational
approximants. From this result we argue the existence of a non-equilibrium
quantum phase transition with a critical phase $|\Delta|\leqslant1$. From the
non-superextensivity of the Fisher information of reduced states, we infer that
this non-equilibrium quantum phase transition does not have local order
parameters but has non-local ones, at least at $|\Delta|=1$. In the
non-perturbative regime for the noise strength, we numerically computed the
reduced Fisher information which lower bounds the full state Fisher
information, and is superextensive only at $|\Delta|=1$. Form the latter
result, we derived local order parameters at $|\Delta|=1$ in the
non-perturbative case. The existence of critical behaviour witnessed by the
Fisher information in the phase $|\Delta|<1$ is still an open problem. The
Fisher information also represents the best sensitivity for any estimation of
the control parameter, in our case the anisotropy $\Delta$, and its
superextensivity implies enhanced estimation precision which is also highly
robust in the presence of a critical phase.

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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga