On subregion action complexity in AdS3 and in the BTZ black hole

We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.

Section: Reduced Density Matricesmentioning

confidence: 99%

Complexity of mixed Gaussian states from Fisher information geometry

Giulio

Tonni

2020

“…For details see[73][74][75][76][77][78][79] and references therein 3. It is worth noting that in their paper, the authors argued that for a gravitating bath, one does not get a Page curve and instead end up with a constant entanglement curve.…”

mentioning

confidence: 99%

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

Bhattacharya

Bhattacharyya

Nandy

et al. 2021

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in d-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

“…To resolve the issue, we applied the proposal of ref. [19] (see also [27]) for two-sided AdS black holes in Einstein gravity, and included timelike counterterms given in eq. (1.3) and the GHY term, i.e.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, the above counterterms are applied in the calculation of the subregion action-complexity for an interval in a BTZ black brane background in ref. [27], where it was observed that after the addition of the timelike counterterms given in eq. (1.3), the finite and divergent terms of the subregion action-complexity in the two regularizations are equal to each other up to a finite term −c 3π 2 logL L .…”

Section: Jhep07(2020)020mentioning

confidence: 99%

See 1 more Smart Citation

Regularizations of action-complexity for a pure BTZ black hole microstate

Omidi

2020

In the action-complexity proposal there are two different methods to regularize the gravitational on-shell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them for a pure BTZ black hole microstate. The microstate is obtained from a two-sided BTZ black hole truncated by a dynamical timelike ETW brane. Moreover, it is dual to a finite energy pure state in a two-dimensional CFT. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the Gibbons-Hawking-York term on the timelike boundary of the WDW patch, which exists in one of the regularizations, the coefficients of the UV divergent terms of action-complexity in the two methods become equal to each other. Furthermore, we compare the finite terms of action-complexity in both regularizations, and show that when the UV cutoff surface is close enough to the asymptotic boundary of the bulk spacetime, action-complexities in both regularizations become exactly equal to each other.