On the time dependence of holographic complexity
By Dean Carmi, Shira Chapman, H. Marrochio, R. Myers, Sotaro Sugishita. 2017
302 citations recorded by the source corpus.
A bstractWe evaluate the full time dependence of holographic complexity in various eternal black hole backgrounds using both the complexity=action (CA) and the complexity=volume (CV) conjectures. We conclude using the CV conjecture that the rate of change of complexity is a monotonically increasing function of time, which saturates from below to a positive constant in the late time limit. Using the CA conjecture for uncharged black holes, the holographic complexity remains constant for an initial period, then briefly decreases but quickly begins to increase. As observed previously, at late times, the rate of growth of the complexity approaches a constant, which may be associated with Lloyd’s bound on the rate of computation. However, we find that this late time limit is approached from above, thus violating the bound. For either conjecture, we find that the late time limit for the rate of change of complexity is saturated at times of the order of the inverse temperature. Adding a charge to the eternal black holes washes out the early time behaviour, i.e. complexity immediately begins increasing with sufficient charge, but the late time behaviour is essentially the same as in the neutral case. We also evaluate the complexity of formation for charged black holes and find that it is divergent for extremal black holes, implying that the states at finite chemical potential and zero temperature are infinitely more complex than their finite temperature counterparts.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4ccb38dde320fd1002314bbe6221c6fdd2d771cc
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Citations in the corpus
- Circuit complexity in quantum field theory (2017, background): “In particular, we emphasize that with the choice ω0 = e −σ/δ, the UV cut-off appears in infrared contributions to the holographic complexity arising from joint terms deep in the bulk [19, 23].”
- Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “Immediately after tc1, there is a negative spike in the rate of growth, which is similar to the one found for the eternal BTZ black hole with the inclusion of the counterterm in appendix A of [23].”
- Circuit complexity for free fermions (2018, background): “e UV divergences, which is determined by contributions coming from the asymptotic regions of the bulk spacetime. One explicit example of this behaviour is provided with the complexity of formation in [11,13]. However, our new results for excited states in the free fermionic eld theory provide some a”
- Holographic complexity in Vaidya spacetimes. Part I (2018, methodology): “If we fix the profile fp(v) = ω d−2 to be a fixed constant, these metrics would correspond precisely to the black hole geometries in d ≥ 3 for which the holographic complexity was studied in [34, 46].”
- Islands in Schwarzschild black holes (2020, methodology): “Numerically, we can easily find that V (t) grows linearly in time at late times, as in the case of the holographic complexity [44].”
- Complexity and entanglement for thermofield double states (2018, background): “k hole exhibits non-universal behaviour at early times due to the normalization of the null normals to the boundary of the Wheeler-DeWitt patch in the complexity=action proposal. As discussed in ref. [28], the transient behaviour of the time derivative is controlled by a dimensionless parameter , as”