Anti-de Sitter plane wave backgrounds are dual to conformal field theory excited states with energy momentum density ${T}_{++}=Q$. Building on previous work on entanglement entropy in these and nonconformal brane plane wave backgrounds, we first describe a phenomenological scaling picture for entanglement in terms of ``entangling partons.'' We then study aspects of holographic mutual information in these backgrounds for two strip shaped subsystems, aligned parallel or orthogonal to the flux. We focus on the wide ($Q{l}^{d}\ensuremath{\gg}1$) and narrow ($Q{l}^{d}\ensuremath{\ll}1$) strip regimes. In the wide strip regime, mutual information exhibits growth with the individual strip sizes, and a disentangling transition as the separation between the strips increases, for which the behavior is distinct from the ground and thermal states. In the narrow strip case, our calculations have parallels with ``entanglement thermodynamics'' for these anti-de Sitter plane wave deformations. We also discuss some numerical analyses.
Anti-de Sitter plane wave backgrounds are dual to conformal field theory excited states with energy momentum density T++=Q. Building on previous work on entanglement entropy in these and nonconformal brane plane wave backgrounds, we first describe a phenomenological scaling picture for entanglement in terms of entangling partons.'' We then study aspects of holographic mutual information in these backgrounds for two strip shaped subsystems, aligned parallel or orthogonal to the flux. We focus on the wide ($Q{l}^{d}\ensuremath{\gg}1$) and narrow ($Q{l}^{d}\ensuremath{\ll}1$) strip regimes. In the wide strip regime, mutual information exhibits growth with the individual strip sizes, and a disentangling transition as the separation between the strips increases, for which the behavior is distinct from the ground and thermal states. In the narrow strip case, our calculations have parallels with entanglement thermodynamics'' for these anti-de Sitter plane wave deformations. We also discuss some numerical analyses.
We study various entanglement measures associated with certain nonconformal field theories. We consider nonconformal Dp-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in p=1, 2, 4, we explicitly compute properties of holographic entanglement entropy and the entanglement wedge cross section, EW, corresponding to two parallel strip shaped boundary subregions in these setups. We study low and high temperature behaviors of these quantities analytically as well as by using numerical methods. In all cases, the EW decreases monotonically with temperature. We observe discontinuous jumps in EW, while the width of (as well as the separation between) the subregions reaches critical values in all the cases considered. However, the corresponding holographic mutual information IM continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\mathrm{E}}_{W}\ensuremath{\ge}{\mathtt{I}}_{M}/2$ still holds for nonconformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.
We study thermodynamics of entanglement entropy for weakly excited states in certain nonconformal field theories, whose gravity duals are given by nonconformal Dp-branes. We observe that the entanglement entropy of a sufficiently small system in nonconformal backgrounds still obeys a first-law-like relation, just as the anti--de Sitter counterparts investigated in [J. Bhattacharya, M. Nozaki, T. Takayanagi, and T. Ugajin, Phys. Rev. Lett. 110, 091602 (2013)]. The effective temperature is proportional to the inverse of the size of the subsystem. The proportionality is a dimensionless constant which is only determined by the shape of the entangling region and independent of any coupling. This universality is confirmed by working with the 10-dimensional string frame metric as well as the lower-dimensional effective metric. When the entangling region is a strip and translational invariance is broken by metric fluctuations, we derive a first-law-like relation where additional components of the stress energy tensor are involved.
The AdS/CFT correspondence, a remarkable duality between certain gravitational theories in anti-de Sitter (AdS) spacetime and quantum field theories with conformal symmetry (CFT), has had a profound effect on the development of theoretical physics in the past two decades. Recently, many connections of AdS/CFT to quantum information theory have been found, in particular by providing gravitationally dual descriptions of various entanglement measures. Understanding these manifestions of AdS/CFT --- or more generally, the conjectured holographic principle encompassing it --- requires the combination of tools from both high-energy theory and quantum information physics. In this cumulative thesis, the convergence between these two fields is approached from two fronts: First, by calculations within the dual gravitational theory, and second, using a tensor network ansatz to describe the quantum states suspected to possess such a gravitational description. In the first approach, using the gravitational side of AdS/CFT, entanglement entropies of complicated 2+1-dimensional excited CFTs are computed, thus showing how the holographic approach provides access to systems previously out of reach of practical methods, while introducing new numerical methods that this approach necessitates. The second approach is given by tensor networks, a highly successful ansatz for computing properties of one- and two-dimensional quantum systems. Efficiently computable classes of tensor networks are tested in their ability to represent simple holographic systems, successfully reproducing both hyperbolic geometrical features as well as critical boundary states. In addition, the general properties of tensor networks on regular hyperbolic tesselations are considered, leading to new connections to models not previously considered in the context of holography. This interplay of different approaches to quantum information holography showcases the richness of this new field and suggests that a wide range of physical phenomena is accessible via the new tools now at our disposal.
Entanglement entropy is a proposal to quantify quantum entanglement of two disjoint regions in a pure system. It is a relatively new topic and is developing rapidly. The current main motives to study it are its applications to studying quantum gravity, thermalization and phase transitions in condensed matter systems. Mutual information is a related quantity and it can be used to measure the amount of information two disjoint regions share. The purpose of this thesis is to give an introduction to the general results of the field without considering specific systems. The two prominent approaches used are two-dimensional conformal field theory and the holographic entanglement entropy conjecture. The first approach is to calculate entanglement entropy using conformal field theory, the results of which are known to be exact although technically more difficult to derive and only available for 1+1 dimensional systems. Both static and dynamic systems will be discussed. The results are reproduced and generalized to higher dimensions using holography. As a more recent topic, the holographic approach is used to rederive the entanglement entropy of systems with a Fermi surface using AdS/Vaidya metric with Lifshitz scaling and hyperscaling violation. The final chapter of the thesis discusses mutual information in various static and dynamic cases considered in the previous chapters. For the first time, the evolution of mutual information is calculated in AdS/Vaidya metric with Lifshitz scaling and hyperscaling violation in the critical theta=d-1 case.
A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.
We study certain classes of g++ deformations of theories arising in gauge/string realizations of nonrelativistic holography, some of which pertain to z=2 Lifshitz theories while others (pertaining to hyperscaling violation) comprise certain classes of excited states. Building on previous work, we consider holographic entanglement entropy for spacelike strip subsystems in a highly boosted (lightlike) limit, where the strip is stretched along the null x+ plane. The leading divergence in entanglement in this null limit for these excited states is milder than the usual area law for spacelike subsystems in ground states. For ground states, the entanglement vanishes, perhaps consistent with ultralocality. We discuss this briefly from a field theory perspective. We also present some simple free lightfront field theory examples in excited states where correlators are nonvanishing.