Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circuit Complexity for Fermionic Thermofield Double states   Motivated by the holographic complexity proposals, in this paper, we
investigate the time dependence of the complexity for the Fermionic thermofield
double state (TFD) using the Nielsen approach and Fubini-Study (FS) approach
separately. In both two approaches, we discuss the results for different
reference states: the Dirac vacuum state and the Gaussian state which has no
spatial entanglement (NSE). For Dirac vacuum reference state, we find that the
complexity by both two approaches is time independent and the circuit
complexity shares the same expression for both methods with the $L^2$ norm. For
the NSE reference state, the complexity by the Nielsen approach is
time-dependent while it by the FS approach is time-independent. Further, we
find our dynamical results are in good agreement with the bosonic case, where
the complexity evolves in time and saturates after a time at the order of the
inverse temperature. And we show that the complexity of formation is also
shared same similar behaviors with the holographic complexity.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con