TY - JOUR A1 - Erdmenger, Johanna A1 - Fernández, Daniel A1 - Flory, Mario A1 - Megías, Eugenio A1 - Straub, Ann-Kathrin A1 - Witkowski, Piotr T1 - Time evolution of entanglement for holographic steady state formation JF - Journal of High Energy Physics N2 - Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time \(t\) = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case. KW - Physics KW - AdS-CFT Correspondence KW - Gauge-gravity correspondence KW - Holography and condensed matter physics (AdS/CMT) Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-173798 VL - 2017 IS - 10 ER - TY - JOUR A1 - Abt, Raimond A1 - Erdmenger, Johanna A1 - Gerbershagen, Marius A1 - Melby-Thompson, Charles M. A1 - Northe, Christian T1 - Holographic subregion complexity from kinematic space JF - Journal of High Energy Physics N2 - We consider the computation of volumes contained in a spatial slice of AdS(3) in terms of observables in a dual CFT. Our main tool is kinematic space, defined either from the bulk perspective as the space of oriented bulk geodesics, or from the CFT perspective as the space of entangling intervals. We give an explicit formula for the volume of a general region in a spatial slice of AdS(3) as an integral over kinematic space. For the region lying below a geodesic, we show how to write this volume purely in terms of entangling entropies in the dual CFT. This expression is perhaps most interesting in light of the complexity = volume proposal, which posits that complexity of holographic quantum states is computed by bulk volumes. An extension of this idea proposes that the holographic subregion complexity of an interval, defined as the volume under its Ryu-Takayanagi surface, is a measure of the complexity of the corresponding reduced density matrix. If this is true, our results give an explicit relationship between entanglement and subregion complexity in CFT, at least in the vacuum. We further extend many of our results to conical defect and BTZ black hole geometries. KW - AdS-CFT Correspondence KW - Gauge-gravity correspondence KW - Black Holes in String Theory KW - Black-hole KW - Entanglement Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-227711 VL - 1 IS - 12 ER - TY - JOUR A1 - Abt, Raimond A1 - Erdmenger, Johanna T1 - Properties of modular Hamiltonians on entanglement plateaux JF - Journal of High Energy Physics N2 - The modular Hamiltonian of reduced states, given essentially by the logarithm of the reduced density matrix, plays an important role within the AdS/CFT correspondence in view of its relation to quantum information. In particular, it is an essential ingredient for quantum information measures of distances between states, such as the relative entropy and the Fisher information metric. However, the modular Hamiltonian is known explicitly only for a few examples. For a family of states rho(lambda) that is parametrized by a scalar lambda, the first order contribution in (lambda) over tilde = lambda-lambda(0) of the modular Hamiltonian to the relative entropy between rho(lambda) and a reference state rho(lambda 0) is completely determined by the entanglement entropy, via the first law of entanglement. For several examples, e.g. for ball-shaped regions in the ground state of CFTs, higher order contributions are known to vanish. In these cases the modular Hamiltonian contributes to the Fisher information metric in a trivial way. We investigate under which conditions the modular Hamiltonian provides a non-trivial contribution to the Fisher information metric, i.e. when the contribution of the modular Hamiltonian to the relative entropy is of higher order in (lambda) over tilde. We consider one-parameter families of reduced states on two entangling regions that form an entanglement plateau, i.e. the entanglement entropies of the two regions saturate the Araki-Lieb inequality. We show that in general, at least one of the relative entropies of the two entangling regions is expected to involve (lambda) over tilde contributions of higher order from the modular Hamiltonian. Furthermore, we consider the implications of this observation for prominent AdS/CFT examples that form entanglement plateaux in the large N limit. KW - AdS-CFT Correspondence KW - Gauge-gravity correspondence KW - Conformal Field Theory KW - Relative Entropy KW - Complexity Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-227693 VL - 11 IS - 2 ER -