Circuit complexity for fermionic thermofield double states

Jiang, Jie; Liu, Xiangjing

doi:10.1103/physrevd.99.026011

Cited by 44 publications

(42 citation statements)

References 58 publications

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“…Here and below, it should not be confused that we always use E µνρσ to denote the tensor associated to a single curvature polynomial. From these results, it is straightforward to derive the Noether charge (58) for Einstein-Gauss-Bonnet gravity. We rewrite the result as follows…”

Section: Resultsmentioning

confidence: 99%

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Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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We study the general time dependence of complexity for holographic states dual to Lovelock black holes using the "Complexity=Action" (CA) proposal. We observe that at early times, the critical time at which the complexity begins to increase is a decreasing function of the higher order coupling constants, which implies that the complexity evolves faster than that of Schwarzschild black holes. At late times, the rate of change of complexity is essentially determined by the generalised Gibbons-Hawking-York boundary term evaluated at the future singularity. In particular, its ratio to black hole mass is a characteristic constant, independent of the higher order couplings. Thus, in the vanishing coupling limit, the result in general does not reduce to that of Schwarzschild black holes, in spite of that the metric reduces to the latter as well as the gravitational action. In fact, the two differ by a constant during the whole time evolution. Including the next-to-leading order term around late times, we find that as the Einstein case, the late time limit is always approached from above, thus violating any conjectured upper bound given by the late time result. For charged Lovelock black holes, we find that with sufficient charge, the complexity roughly behaves the same as the Einstein case. However, for smaller charges, the two have some significant differences. In particular, unlike the Einstein case, in the uncharged limit the complexity growth rate does not match with the neutral case, differing by a constant in the whole time evolution.

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Section: Resultsmentioning

confidence: 99%

“…This motivates people to search new proposals for complexity [47,48,49]. In addition, the active research in holography promotes studies of complexity for quantum field theories [50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66] as well as in condensed matter physics [67].…”

Section: Introductionmentioning

confidence: 99%

Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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“…This approach was first applied to a concrete quantum field theory calculation in [57], where the authors adapted Nielsen's approach to evaluate the complexity of the vacuum state of a free scalar field theory. These calculations have been extended in a number of interesting ways in the past few years, e.g., [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], but we will be particularly interested in [65] where the same techniques were applied to explore the complexity of coherent states in the same QFT.…”

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confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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We investigate the first law of complexity proposed in [1], i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

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“…which gives the same result as (27) by the BRSSZ method. Moreover, this result reveals that the difference between these two methods only comes from the boundary term of the segments on the horizon for the calculation of late-time rate.…”

Section: Late-time Complexity Growth Ratementioning

confidence: 68%

Investigating two counting methods of the holographic complexity

Jiang

2019

Phys. Rev. D

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We investigated the distinction between two kinds of "Complexity equals Action"(CA) conjecture counting methods which are separately provided by Brown et al. and Lehner et al. separately. For the late-time CA complexity growth rate, we show that the difference between two counting methods only comes from the boundary term of the segments on the horizon. However, both counting methods give the identical late-time result. Our proof is general, independent of the underlying theories of higher curvature gravity as well as the explicit stationary spacetime background. To be specific, we calculate the late-time action growth rate in SAdS black hole for F(Ricci) gravity, and show that these two methods actually give the same result. Moreover, by using the Iyer-Wald formalism, we find that the full action rate within the WDW patch can be expressed as some boundary integrations, and the final contribution only comes from the boundary on singularity. Although the definitions of the mass of black hole has been modified in F(Ricci) gravity, its late-time result has the same form with that of SAdS black hole in Einstein gravity. arXiv:1905.08447v1 [hep-th]

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Circuit complexity for fermionic thermofield double states

Cited by 44 publications

References 58 publications

Time dependence of complexity for Lovelock black holes

Time dependence of complexity for Lovelock black holes

Aspects of the first law of complexity

Investigating two counting methods of the holographic complexity

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