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Circuit Complexity for Fermionic Thermofield Double states

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arxiv 1812.00193 v1 pith:QVLLUR3B submitted 2018-12-01 hep-th

Jie Jiang , Xiangjing Liu This is my paper · ORCID
classification hep-th
keywords complexitystateapproachtimereferenceapproachescircuitdirac
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Complexity measures in QFT and constrained geometric actions

    hep-th 2019-08 reject novelty 7.0 of 10

    The authors claim to rule out inhomogeneous complexity costs such as F_kappa and F_sigma^2 and to single out F_⟨H^2⟩ as the canonical complexity measure, but the no-go proof is incomplete.

  2. Time dependence of complexity for Lovelock black holes

    hep-th 2019-08 conditional novelty 6.0 of 10

    For Lovelock black holes, the Complexity=Action growth rate at late times is a coupling-independent multiple of the mass, and the Schwarzschild limit is recovered only up to a constant under the authors' boundary-term...

  3. Reflections on Virasoro circuit complexity and Berry phase

    hep-th 2019-08 reject novelty 3.0 of 10

    A claimed identification of Virasoro circuit complexity with the Berry connection fails a basic consistency check for pure rotations.

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