Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically
  Quantum Ordered Systems   Are systems that display Topological Quantum Order (TQO), and have a gap to
excitations, hardware fault-tolerant at finite temperatures? We show that in
surface code models that display low d-dimensional Gauge-Like Symmetries, such
as Kitaev's and its generalizations, the expectation value of topological
symmetry operators vanishes at any non-zero temperature, a phenomenon that we
coined thermal fragility. The autocorrelation time for the non-local
topological quantities in these systems may remain finite even in the
thermodynamic limit. We provide explicit expressions for the autocorrelation
functions in Kitaev's model. If temperatures far below the gap may be achieved
then these autocorrelation times, albeit finite, can be made large. The
physical engine behind the loss of correlations at large spatial and/or
temporal distance is the proliferation of topological defects at any finite
temperature as a result of a dimensional reduction. This raises an important
question: How may we best quantify the degree of protection of quantum
information in a topologically ordered system at finite temperature?

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The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph