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A global quench is an interesting setting where we can study thermalization of subsystems in a pure state. We investigate entanglement entropy (EE) growth in global quenches in holographic field theories and relate some of its aspects to quantities characterizing chaos. More specifically we obtain four key results: In a companion paper [1], these results are put in the broader context of EE growth in chaotic systems: we relate EE growth to the chaotic spreading of operators, derive bounds on EE at a given time, and compare the holographic results to spin chain numerics and toy models. In this paper, we perform holographic calculations that provide the basis of arguments presented in that paper. [ABSTRACT FROM AUTHOR]

Relative entropy of entanglement (REE) is an entanglement measure of bipartite mixed states, defined by the minimum of the relative entropy S(ρAB ||σAB ) between a given mixed state ρAB and an arbitrary separable state σAB. The REE is always bounded by the mutual information IAB = S(ρAB ||ρA ⊗ ρB) because the latter measures not only quantum entanglement but also classical correlations. In this paper we address the question of to what extent REE can be small compared to the mutual information in conformal field theories (CFTs). For this purpose, we perturbatively compute the relative entropy between the vacuum reduced density matrix ρAB0 on disjoint subsystems A ∪ B and arbitrarily separable state σAB in the limit where two subsystems A and B are well separated, then minimize the relative entropy with respect to the separable states. We argue that the result highly depends on the spectrum of CFT on the subsystems. When we have a few low energy spectrum of operators as in the case where the subsystems consist of finite number of spins in spin chain models, the REE is considerably smaller than the mutual information. However in general our perturbative scheme breaks down, and the REE can be as large as the mutual information. [ABSTRACT FROM AUTHOR]

In this paper, we study a possibility where gravity and time emerge from quantum matter. Within the Hilbert space of matter fields defined on a spatial manifold, we consider a sub-Hilbert space spanned by states which are parameterized by spatial metric. In those states, metric is introduced as a collective variable that controls local structures of entanglement. The underlying matter fields endow the states labeled by metric with an unambiguous inner product. Then we construct a Hamiltonian for the matter fields that is an endomorphism of the sub-Hilbert space, thereby inducing a quantum Hamiltonian of the metric. It is shown that there exists a matter Hamiltonian that induces the general relativity in the semi-classical field theory limit. Although the Hamiltonian is not local in the absolute sense, it has a weaker notion of locality, called relative locality : the range of interactions is set by the entanglement present in target states on which the Hamiltonian acts. In general, normalizable states are not invariant under the transformations generated by the Hamiltonian. As a result, a physical state spontaneously breaks the Hamiltonian constraint, and picks a moment of time. The subsequent flow of time can be understood as a Goldstone mode associated with the broken symmetry. The construction allows one to study dynamics of gravity from the perspective of matter fields. The Hawking radiation corresponds to a unitary evolution where entanglement across horizon is gradually transferred from color degrees of freedom to singlet degrees of freedom. The underlying quantum states remain pure as evaporating black holes keep entanglement with early Hawking radiations in the singlet sector which is not captured by the Bekenstein-Hawking entropy. [ABSTRACT FROM AUTHOR]

We study the entanglement wedge cross-section (EWCS) in holographic massive gravity theory, in which a first and second-order phase transition can occur. We find that the mixed state entanglement measures, the EWCS and mutual information (MI) can characterize the phase transitions. The EWCS and MI show exactly the opposite behavior in the critical region, which suggests that the EWCS captures distinct degrees of freedom from that of the MI. More importantly, EWCS, MI and HEE all show the same scaling behavior in the critical region. We give an analytical understanding of this phenomenon. By comparing the quantum information behavior in the thermodynamic phase transition of holographic superconductors, we analyze the relationship and difference between them and provide two mechanisms of quantum information scaling behavior in the thermodynamic phase transition. [ABSTRACT FROM AUTHOR]

Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both the dual order-parameter field and the metric tensor field originate from density-density and energy-momentum tensor-tensor effective interactions, respectively, in the recursive renormalization group transformation, performed approximately in the Gaussian level. This linear approximation in the recursive renormalization group transformation for the gravity sector gives rise to a linearized quantum Einstein-scalar theory along the z-directional emergent space. In the large N limit, where N is the flavor number of the original scalar fields, quantum fluctuations of both dynamical metric and dual scalar fields are suppressed, leading to a classical field theory of the Einstein-scalar type in (D+1)-spacetime dimensions. We show that this emergent background gravity describes the renormalization group flows of coupling functions in the UV quantum field theory through the extra dimension. More precisely, the IR boundary conditions of the gravity equations correspond to the renormalization group β-functions of the quantum field theory, where the infinitesimal distance in the extra-dimensional space is identified with an energy scale for the renormalization group transformation. Finally, we also show that this dual holographic formulation describes quantum entanglement in a geometrical way, encoding the transfer of quantum entanglement from quantum matter to classical gravity in the large N limit. We claim that this entanglement transfer serves as a microscopic foundation for the emergent holographic duality description. [ABSTRACT FROM AUTHOR]

We study the spread of Rényi entropy between two halves of a Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield double (TFD) state. The SYK chain model is a model of chaotic many-body systems, which describes a one-dimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer Rényi index n > 1, the Rényi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly-AdS gravity. [ABSTRACT FROM AUTHOR]

We discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two constraints: one follows from the existence of an emergent light cone, and the other is a conjecture associated to the 'entanglement velocity' v . We compare this model to new holographic and spin chain computations, and to an operator growth picture. Finally, we introduce a second way of computing the emergent light cone speed in holographic theories that provides a boundary dynamics explanation for a special case of entanglement wedge subregion duality in AdS/CFT. [ABSTRACT FROM AUTHOR]

A closed formula of the universal part of supersymmetric Rényi entropy S for six-dimensional (1, 0) superconformal theories is proposed. Within our arguments, S across a spherical entangling surface is a cubic polynomial of ν = 1/ q, with 4 coefficients expressed as linear combinations of the 't Hooft anomaly coefficients for the R-symmetry and gravitational anomalies. As an application, we establish linear relations between the c-type Weyl anomalies and the 't Hooft anomaly coefficients. We make a conjecture relating the supersymmetric Rényi entropy to an equivariant integral of the anomaly polynomial in even dimensions and check it against known data in 4 d and 6 d. [ABSTRACT FROM AUTHOR]

Quantum corrections to the entanglement entropy of matter fields interacting with dynamical gravity have proven to be very important in the study of the black hole information problem. We consider a one-particle excited state of a massive scalar field infalling in a pure AdS3 geometry and compute these corrections for bulk subregions anchored on the AdS boundary. In the dual CFT2, the state is given by the insertion of a local primary operator and its evolution thereafter. We calculate the area and bulk entanglement entropy corrections at order O N 0 , both in AdS and its CFT dual. The two calculations match, thus providing a non-trivial check of the FLM formula in a dynamical setting. Further, we observe that the bulk entanglement entropy follows a Page curve. We explain the precise sense in which our setup can be interpreted as a simple model of black hole evaporation and comment on the implications for the information problem. [ABSTRACT FROM AUTHOR]

Recently we pointed out that the black hole interior operators can be reconstructed by using the Hayden-Preskill recovery protocols. Building on this observation, we propose a resolution of the firewall problem by presenting a state-independent reconstruction of interior operators. Our construction avoids the non-locality problem which plagued the "A = RB " or "ER = EPR" proposals. We show that the gravitational backreaction by the infalling observer, who simply falls into a black hole, disentangles the outgoing mode from the early radiation. The infalling observer crosses the horizon smoothly and sees quantum entanglement between the outgoing mode and the interior mode which is distinct from the originally entangled qubit in the early radiation. Namely, quantum operation on the early radiation cannot influence the experience of the infalling observer since description of the interior mode does not involve the early radiation at all. We also argue that verification of quantum entanglement by the outside observer does not create a firewall. Instead it will perform the Hayden-Preskill recovery which saves an infalling observer from crossing the horizon. [ABSTRACT FROM AUTHOR]